{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/jermwatt/machine_learning_refined/blob/main/notes/3_First_order_methods/3_2_First.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iKcl0GdUOXCw"
   },
   "source": [
    "## Chapter 3: First order methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains interactive content from an early draft of the university textbook <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main\">\n",
    "Machine Learning Refined (2nd edition) </a>.\n",
    "\n",
    "The final draft significantly expands on this content and is available for <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main/chapter_pdfs\"> download as a PDF here</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uk01aH8IOXCx"
   },
   "source": [
    "# 3.2 The First-Order Optimality Condition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z_9TU3FmOXCx"
   },
   "source": [
    "In this Section we discuss the foundational first order concept on which many practical optimization algorithms are built: the first order optimality condition.  The first order analog of the zero order condition discussed in the previous Chapter, the first order condition codifies the consistent behavior of how any differentiable function's first derivative(s) behave at its minima.  While there are a few important instances when this tool can be used to directly determine the minima of a function (which we review here), in and of itself the first order optimality condition is more broadly useful because it helps its formal characterization of minimum points serves helps motivate the construction of both first and second order optimization algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "PwCYcJhHOXCy",
    "outputId": "fdc3db3d-0ddc-488a-d2ca-a204cdbd078e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: github-clone in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (1.2.0)\n",
      "Requirement already satisfied: requests>=2.20.0 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (2.32.3)\n",
      "Requirement already satisfied: docopt>=0.6.2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (0.6.2)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.4.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.10)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2.2.3)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2024.12.14)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m24.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.3.1\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n",
      "chapter_3_library already cloned!\n"
     ]
    }
   ],
   "source": [
    "# install github clone - allows for easy cloning of subdirectories\n",
    "!pip install github-clone\n",
    "from pathlib import Path \n",
    "\n",
    "# clone library subdirectory\n",
    "if not Path('chapter_3_library').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/3_First_order_methods/chapter_3_library\n",
    "else:\n",
    "    print('chapter_3_library already cloned!')\n",
    "\n",
    "# append path for local library, data, and image import\n",
    "import sys\n",
    "sys.path.append('./chapter_3_library')\n",
    "\n",
    "# import section helper\n",
    "import section_3_2_helpers\n",
    "plotter = section_3_2_helpers.Visualizer()\n",
    "\n",
    "# standard imports\n",
    "import matplotlib.pyplot as plt\n",
    "import copy\n",
    "\n",
    "# import autograd-wrapped numpy\n",
    "import autograd.numpy as np\n",
    "\n",
    "# this is needed to compensate for matplotlib notebook's tendancy to blow up images when plotted inline\n",
    "%matplotlib inline\n",
    "from matplotlib import rcParams\n",
    "rcParams['figure.autolayout'] = True\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fRU4pY_WOXCz"
   },
   "source": [
    "##  The first order condition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xHksba07OXCz"
   },
   "source": [
    "In the next Python cell we plot a quadratic functions in two and three dimensions, and mark the global minimum point on each with a green point.  In each panel we also draw the first order Taylor series approximation - a tangent line/hyperplane - generated by the first derivative(s) at the function's minimum value (see Appendix Chapter A for further details on Taylor series approximations).  In terms of the behavior of the first order derivatives here we see - in both instances - that the tangent line/hyperplane is perfectly flat, indicating that the first derivative(s) is exactly zero at the function's minimum.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 225
    },
    "id": "jIIMCHsLOXCz",
    "outputId": "d387106e-41c7-4b14-8297-cbd0109b03e7"
   },
   "outputs": [
    {
     "data": {
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lmM1mIiMjmTBhAhaLhTVr1pzhaEPv66+/BpoP4gpqbGzE6XRK8u+AkPxkxsXFqT3//X4/f/jDH0IRhuhmPv/88xbd/GRf/6nrCuv6x5Obm4tOp2Pr1q14vd6QxNDU1ER5eTlpaWn07t2bjIwMli9f3qHHVlVVqYcARUdHM3jwYFauXHlCdQNdTWlpKdu2bWP69OktjuytqKgAkGn/DgjZZfk999zToue/nE0tzqRAIMDvf/979evHHnusS4xKOzNFUbrEuv7xhIeHk5aWRn19PTt37gxJDIcPH8bj8ZCamopGo2Hs2LGUlpZSUlJyzMcFAgEqKiro0aOHetuoUaMIBAIsXrz4TIcdEn6/nwULFpCSksLo0aNbfK+8vJyoqCiioqJCFF3XEbLfflFRUfz2t79Vvz7yF7MQp9uHH36o/mIfO3as9PA/TbRabZdY1z+e8ePH4/P5WLVqVUj2yhcVFWEymdSt0OPGjSM6OpqvvvrqmI+rr6/Hbre3OLfeaDQyceJEtm/fTn5+/pkMOyReeuklNmzYwMyZM1tdwMt6f8eFdOhzxx13qP9Qn3/+eafYbiPOPR6Ph0ceeUT9+vHHH+/Siaqz0Gg0XWZd/3j69OmD2WymoKAgJN1HCwoK1Kl7aE7gI0eOZMeOHdjt9nYfV1JSgs/no0+fPi1uz83NJTExkYULF55TxX/19fVs3boVk8lETk5Oi+8pikJ5eTkZGRkhiq5rCelPrclkalGA9fDDD3fLDlXizHr11VcpLCwEYObMmZx//vkhjkh0NikpKaSlpWGxWNTdIKfTsX6v2e12SktLWyWtyZMnq3v321NWVoZOp2u1xq3RaJg2bRpVVVXnzKl/iqLw2Wef4XA4yMzMbHXRWV9fj9PplOTfQSG/ZL/pppvUK7gVK1acs+tUIjRsNhuPPfaY+vWTTz4po37RikajYejQoWg0GjZu3Hhai+WO9//t0KFDeDyeVtPVCQkJDBw4kLVr1+Lz+dp8bHl5OUlJSW3OvsTGxjJixAhWrlxJWVnZyb+BTmLjxo0UFRXhdDrJyspq9f3ge5Rp/44JefI3Go0tOv099NBD+P3+EEYkziVPPfUUNTU1AMybN49Ro0aFOCLRWfXr14+oqChqa2tZv379WXvdwsJCzGZzmx3ppkyZgtvtZu3atW0+try8nMzMzHafe+TIkZjNZj755JN2LyC6gtraWpYtW8aIESMIBAJtvud33nmHkpIS6ezXQSFP/gBz585lzJgxQPPBFvPnzw9xROJcUFlZyT/+8Q8A9Hp9i1P8hDhaTk4OCQkJuN1uvv32W1wu1xl/TUVR2LdvX7tb03JycujVqxfLli1r1fTHZrNRX19Pr1692n1+rVbLzJkzKSkp6bLH/vp8Pj7++GNiYmLUFr49e/ZscZ/q6mq+//57GTiegE6R/DUaDX//+9/Vrx999FEcDkcIIxLngscff5ympiYAfvGLX9C7d+8QRyQ6M71ez9ChQ4mKiqK6uprNmzef8desqamhpqbmmKP3yZMnY7FY+P7771vcXlxc3Gax39ESEhIYPXo033zzjVr7cibY7XbefPPN095fYPny5VRXV3PVVVeRn5+P0WhssbsB4K233sJkMnHddded1tc+l3WK5A8wdepULrvsMqB57ebZZ58NcUSiK8vPz+fVV18FIDIyskVhqRDtGTRoEFqtFpPJxKpVq874VHl+fj6BQOCYTWmGDh1Keno6ixYtanF7cXExGo2mVSJsy4gRI0hISOCtt946Y81/vvvuO/bu3cuePXtO23Pu27eP7777jlmzZpGWlkZBQQHx8fHExsaq97FYLKxevZqkpCSGDh162l77XNdpkj/AX//6V7Vw5YknnlDXaoU4UQ8++KD6i/vXv/41ycnJIY5IdAV9+/YlNjYWs9lMUVHRGW8+tn//fhITE495uJRGo+G8886jtLS0RSv0srKydov92nqOmTNnsmLFCn7/+9+f9pP/3G4369evx+FwqEfqnqq6ujo+/fRTBgwYwLhx44Dm4sijp/zffvttYmJiSEpKIiUl5bS8dnfQqZL/wIEDufnmm4HWVdpCdNTy5cv5/PPPgeY2nw888ECIIxJdRVhYGMOHD8dmsxEZGcnKlSvP2BG5TqeT/Pz8Ft352jNmzBiSkpJYuHCheltpaWmHHhtks9kICwvD7/ezYsWKk4q5PZs3b6axsZFevXqdlj4JLpeLd999l6ioKC6//HJ1x0R1dXWLJRKLxcLKlStJSkpS2zSLjulUyR+aD1sJVmu+9NJL7N69O8QRia7E7/dz3333qV8/8cQTatc0ITpiyJAheDweevTowYEDB9i7d+9ped6j9/qvX7+e4uLiNretHU2v13Peeedx8OBBDh06RGNjIw0NDWoBXEccPHgQvV7PyJEj+frrr9m1a9cJv4e2eL1eVq9eTXZ2Njk5OVRVVam1NifD7/fz4YcfYrfbmTdvHmFhYUBzonc4HC1G/m+99RbR0dFER0e3mhEQx9bpkn9aWpra9jf4i1wa/4iOeuONN9Q2vqNHj+YnP/lJiCMSXU3//v1JSEjAbrdjNBr55ptvzsjvoC+++ILCwsIOJ8oJEyaQkJDAf//7Xw4dOoTX62XAgAEdfr2ioiIiIyOZPXs2OTk5fPzxx8c9O6Ajtm3bRk1NjXq0rs/no7S09KSeS1EU8vLyOHToEHPnziUhIUH93q5duzAajWpfmNraWlavXs3YsWPR6/UduogSP+h0yR+a12iDV3HLli1rMdUlRHsaGxv53e9+p379zDPPnBOtZ8XZZTQaSU9PZ+XKlfTt25c9e/ac9h75Xq8XnU5HeHh4h7fgGY1GzjvvPPLz89mwYQMGg+GETq8rLS0lPT0drVbL+eefT3R0NAsWLDil2iqfz8fKlSvJysoiJiaGqKgojEbjSV9ULF++nK1btzJnzpxW7Xv37t1LZGSk2sHvtddeIy4ujmHDhqHRaE5oCUR00uRvMpl46qmn1K/vv/9+3G53CCMSXcGf//xn9RfZj370IyZNmhTiiERXFRMTg9PppLq6Gp1Ox7Jly07r6D8/Px+3201OTg5bt27t8K6CSZMmkZCQwMaNG0lNTT2hi9uamhq1+51er1d3V/373/8+6R0A27Zto6qqSm2epdFoSExMpKio6ISf61//+hdvvfUWs2fPZtiwYa2+X1BQQM+ePdFqtZSUlLBu3TouvPBCLBYLKSkphIeHn9R76K46ZfIHuPrqq5k2bRrQ3AHrmWeeCWk8onMrKChQ/4+EhYXx5JNPhjYg0aXdcMMNREVFsXHjRvr378/u3btP6+h/586dREREMGvWLLxeb4fPEzAajUyePJna2toW59gfj8vlwm63t2h9azKZuOqqq3C73bzxxhtYLJYTeg8+n48VK1aQmZlJXFycentaWhpFRUUdvqBRFIUVK1awZs0aYmJimDBhQpv3Ky8vV6f2X375ZVJTU5kzZw7FxcUd2u4oWuq0yV+j0bSYtv3Tn/5ERUVFiKMSnZGiKNxzzz14vV4AHnjgASn+EadEr9eTnZ1NY2MjYWFhaLXa0zb6d7lc7Nixg+zsbLKyssjMzOTbb7/t8ON79eqF0Whsse3veILFfkdPjUdGRnL11Vfjcrl4/fXXqaqq6vBzbtmyhcrKSrU7a1B6ejoul6tD6/6BQIAvv/ySlStX4nA46Nu3b5v3s9vtNDY2kp2dza5du9i5cydz5szB4/FQX18vyf8kdNrkDzBs2DBuu+02oPkf/ze/+U2IIxKd0Weffaaee56ZmcnDDz8c4ojEueDhhx9Gr9ezfPlyBgwYwK5du05L5f/u3buxWq1qx8mxY8dSUVHBoUOHOvT44uJioqKi8Pv9rbr+tefgwYMYjcY218WjoqKYO3cuiqLw6quvUlBQcNzn83g8fPPNN/Ts2bNFwx2A+Ph4NBrNcbf8Bbfzbd68mYsuuohAINDuiXw7d+7EaDTSu3dvXnrpJXr16sWFF15IUVERGo1GLvZPQqdO/tDcojX4n2vBggWsWrUqtAGJTqWpqYl7771X/frpp5+WrX3itMjJySE9PZ3S0lISEhKor6/nwQcfPOV9/5s3byYhIUHd0jxixAhiY2OPeXTvkQ4fPkxycjLZ2dm8//77HYon+BiTydTm981mM9dccw1xcXG89dZbLFy48JjPu2HDBmpra1uN+qH5PIHk5ORjthKurKzklVdeobi4mOuuu46kpCQURWm3aG/37t1ERESQn59PWVkZP/rRj9Dr9Rw6dIjU1FQ5zOckdPrkn5iYyF/+8hf16zvuuAOPxxPCiERn8uc//1mtLJ49ezZXX311iCMS55LrrrsOv9/P+vXrSUxMpK6u7pQGIFVVVRw4cKBFP36DwcCIESPYs2cPVqv1uM9RUlJCVlaWWuy2cuXK4z6moqLiuOfch4WFMWfOHOLj43nmmWf4xz/+0WYhoMPhYMWKFeTm5hIdHd3mc6WlpVFYWNhq3d/v9/Ptt9/y6quvotfrueWWW+jduzd79+5ts2d/UH5+PhkZGbz99tuMGDGC8ePHoygKhw4darUrQHRMp0/+ALfddpt6hbl3717++c9/hjgi0Rns27dP3RViNBp54YUXjnt2uhAn4vLLLychIYEdO3YwbNgwfD4f77777gn1/D/y/+TGjRsJBAKtRriTJk3CYDCwbNmyYz5XQ0MDdXV19O3bl6FDh9KvXz8+++yzY55AGAgEsFgsHdoKp9VqiYiIwGw2Y7PZeP7551m9erVaTwOwevVqrFbrMY/HzszMxOl0UlxcDDTX5Rw8eJCXX36Zr7/+mrFjx3LzzTcTHx8PNBfsRkVFkZiY2ObzlZaWcujQIXw+Hz/+8Y/RarXU1NRgs9nkwK6T1CWSv06n4+WXX1aL/x577LGT2koizh2KonDXXXepv5QefPDB455uJsSJ0mg0TJ06FafTSVVVldrzf8OGDSf8XA6Hgw0bNrTZhjYmJoYBAwawfv36Y15YFBQU4PP51ANs5syZg9/v59NPP233McHflcc6OfBIhw8fJikpiTvuuINBgwaxdOlSnn76adasWUNZWRlr1qxh0KBBx5xqT0hIQKfTUVBQwIYNG/jLX/7C/PnzMRqN3HLLLcyaNavFeQZFRUVkZ2e3uXUxeMFTX1/PrFmz1GQfLGKU5j4np0skf4CRI0dy1113Ac09se+5554QRyRC6f3332f58uVA89ne//d//xfiiMS56t577yUqKoq1a9eSk5ODxWJh8eLFJ3zs+IYNG7BarfTv37/N70+ePBmv13vMyv/CwkLMZrN6UFWPHj0YN24cK1eubLdSP3gMbq9evToUZ3l5Oenp6YSFhTF9+nRuuukmMjIyWLx4Mb/61a8oKioiJSUFu93eqi5AURRcLhe1tbUEAgFeeeUVnn32Wfbs2cO1117LjTfe2GZjosrKynYvTrZv305DQwPp6ektjuzNz8+nZ8+eGAyGDr0v0VKXSf7QXPwX/I/zxRdfqIe3iO6lrq6uRZHfc889JwU/4owxGo0MHTqUhoYGIiMjURSFAwcOdLgzH4DVauXdd9+lR48e7TajycrKolevXqxYsaLdYrvDhw+3mr6/5JJLiImJ4d///nebjzl06BCJiYntrs8fra6urkV9QGxsLBdddBGXXHIJBoOBPn36UFBQwKpVq3j//fdZu3Yt69evZ926daxevZp169axa9cuTCYTer0ep9PJkCFD6NevX5vLcna7HavV2m7F/n/+8x80Gg0/+clPiIqKApq7eS5fvlyq/E9Bl0r+0dHRPP300+rXd911F42NjSGMSITC/fffr3byu/rqq5kzZ06IIxLnukceeQS9Xk9+fj4GgwGbzcby5cs7vC9+2bJl7NmzB6fTecz7TZo0icbGRrZv397qe1arlaqqqlYzB5GRkVx44YUUFBSwcePGVo8rLS3t8JS/xWLB7Xa3usAIBAKsWbOGnJwcLrroIsaOHYtGo8FoNJKSkkJ8fDyJiYn07NmTAQMGMGbMGC644AJSUlLUUXt79u7di8FgaHP63m63s3btWnr16sWMGTPU25966il1hkKcnC6V/AGuvfZaLrjgAqD5P/VDDz0U4ojE2bRkyRLmz58PNI9Inn/++RBHJLqDuLg4Bg4cyMGDB4Hm8+udTid5eXnHbfxTX1/P9u3bMZvNbNq06Zj3HThwIKmpqSxZsqTV9w4cOIDP52P48OGtvjdp0iT69OnDO++806L4LxAIUFdX1+G+9wcOHMBoNLZKxNu3b+fw4cNMmDABjUaDTqfD5/OpCb9Xr15kZ2eTkZFBQkICYWFhREREoNfrqa6uPua6/J49ewgPD2+z0v/ZZ58lOjqaqVOnqvUALpeLbdu2kZycLHU+p6DLJX+NRsMrr7yi7uV+9dVXT2j6TXRddrud22+/Xf36qaeeOqGDTYQ4Ff/3f/+H1+vFYrFQV1dH79692bx58zGPxlUUhYULF+JwOJg6dSo1NTXHLFbWarVMnDiRioqKVh38CgoKiIyMJCUlpdXjNBoN11xzDX6/n//85z/q7UVFRSiK0uHp8YMHDxIREdHi56qhoYG8vDx69eql1hpAcwFjcBq+PQUFBVit1mPOPBQWFpKZmYnRaGxx+7p169SWv0de8Lz33nvodDpmzpzZofck2tblkj80F3gd2bv9lltuOaXzo0XX8Oijj6pdw4KFSEKcLT179iQnJwev14vVaqWmpoaIiAg+//zzdrfabdiwgc2bNzNy5EhGjhxJVFTUcQcro0ePJjExkby8vBa3FxYWHrNoLyMjgxkzZrBhwwZ2794NNG+HPfIY3OM5fPgwGRkZLXYjvPDCC+zYsYMRI0aot7lcLnw+3zHrCAoKCigrKyM+Pv6YvVmKi4tbXZzY7XaeffZZzGYzMTEx6lKHy+Xik08+IT4+Xp0BFienSyZ/gF/84hdMmTIFaC5oOfIoV3Hu2bBhA88++ywA4eHhvPrqq7KnX5x1f/3rX1EUBY/Hw9q1axk6dCiHDx9uc39+QUEBn376KZmZmaSnp2MwGBg8eDD79u3Dbre3+xo6nY4JEyZQVFSkXuxWVVVRV1fH4MGDjxnfBRdcQM+ePXnttddwuVwcPHiQlJSU447Qg46uuj906BD19fV4vd4WR//W1dWh1WqJiYlp97lWrFgBNHdKbO8cgmBv/qOXBZ588km1HXFGRob6Oh988AEmk4mUlJQO1zGItnXZ5K/Vann99dfVytlnn32W7777LsRRiTPB4XDw05/+VF1bfeyxx8jNzQ1xVKI7Gjt2rFoJX1xcrB4zu2zZsha97L/77jtef/11DAYDI0eOVG8fP3480Nwo51jGjRtHXFycuqNp3759+P3+Fs/VFr1ez7x58wgEArz55puUlpZ2eMrf5XJhtVrV+gCPx8OXX35JSkoKgUCgxdkD9fX1GAyGdpP/4cOH2bt3L3379qVfv37s3r27zR0M+/btQ6vVtpiZ+OKLL9i5cyc//vGP1YZGwfgWLlxIfHw8M2bMkIv/U9Rlkz9Anz59ePzxx4HmtbWf//znMv1/DvrNb36jjhzGjBnDfffdF+KIRHd2//33A81H2m7cuJFdu3Zx+PBhXn75ZbZu3crbb7/NQw89RGFhIVOmTGnRuCYhIYE+ffqwfv36Y/bONxqNjB8/noKCAkpKSti/fz8pKSkdOreiR48ezJ49m61bt55Q8s/Pz0ev16v3D/YOmDJlCvHx8WobbWhO/lFRUW025QH45ptv1IN4+vfvT319fZsHF+3Zs4ewsDA1+R86dIg33niDKVOmMGHCBCwWi3qh/5///AedTkd8fPxxZ0DE8XXp5A9w3333MW7cOKC5UvXBBx8McUTidFq2bBkvvPAC0Hz++IIFC1p0BhPibLvmmmtITk5Go9HgdDqxWq24XC6WLl3KI488wtatWwkLC6O+vr5VJz9oHtU7HA62bdt2zNeZOHEisbGxfPLJJxQVFbXbHKgts2bNIi0tjdLSUsxmc4ceU1BQQFhYGD179qSoqIjvvvuOoUOHEh0dTY8ePSguLlYvWGw2W7vr/aWlpezevZtRo0ap9QZms5mdO3e2uu+BAwfIzMwkIiICl8vFH//4R7Kysrj99tvZtGkTYWFhDBw4ELvdzqJFi0hOTiY9Pf245xSI4+vyyV+n0zF//nz1tKqXXnqJRYsWhTgqcTrU19fz85//XP36b3/7G/369QthREI0u+GGGwgEAhQWFpKSkoKiKAwaNAi9Xs+QIUOYNWsWjY2Nba519+7dm9TU1OMW/oWFhTFp0iT27dtHY2Mjo0eP7nB8Go2G7OxsUlJS+PDDDzt0GNrBgwdJTU1VdyhER0czcOBAAHJzc7FarVRXVxMIBHC5XO1O+S9btgydTsfQoUPVkXpubi47d+5sFUdRURE9e/YkEAjw+OOP4/f7uffee4mMjGTr1q0kJCSQnp7Om2++qS4zjBgxQqb8T4Mun/wB+vbtyz/+8Q/165tuuqlFcYromu655x7KysqA5pHML3/5yxBHJESz++67j7CwMNxuN4FAAK1Wi1arxWQy8e2339K7d29iYmLabNWr1WoZPXo0lZWVxz2jJLivvry8/IRPrysrK6N379643W6effbZ4x79W15eTlZWFkuWLKGuro7zzjtPTbIDBgzA6/Vy8OBB9aS/tpL/4cOH2bVrF7NmzcJqtRIZGYnBYGDAgAHY7fYW2yI9Hg8Wi4WcnBzeeOMN9u7dy80336xO8+/du5cBAwZQW1vL8uXLyczMJCwsrM0+B+LEnRPJH5qr/y+++GKguTL2tttuO27zDdF5ffTRR+p+5ZiYGN5888121xeFONu0Wi3z5s3D7/ezceNG4uLiqK6upl+/ftTW1rJs2TIGDhxIYWFhm11IR44cSUxMTJvNfI6k1+sxGo2YTKZ2K+bbEggEqKqqYuzYsVx99dXs2bOHDz/8sN37B6vu/X4/W7ZsYezYsS3qC6KiooiOjqaoqIi6ujp0Oh2xsbGtnmfZsmUYDAZmz56N1WpVLxCioqJITU1l06ZN6u/l3bt3o9PpKCkp4YsvvuDKK69Uu/jZ7XZqamro27cvL7/8MnFxcaSkpNCvX78OtykWx3bO/DbVaDS88cYb6pGQn332GW+++WaIoxIn49ChQ9xyyy3q1y+88EKHO5QJcbY8+uijage7xMREfD4fDQ0NZGRksHr1amw2Gzqdrs3KfoPBwPDhw8nPz6eurq7d1ygsLAQgLS3tmMn7aGVlZXi9XnJycpg2bRozZ87kq6++anepIXhaYHAavq1+AllZWRw+fJi6ujrMZjNhYWGtnmPPnj1ceOGFGAwGmpqaWlwgDBkyhKKiIkpLSwHYsWMHfr+fL7/8kilTpvCTn/xEve/GjRsxGAyYTCY2bdrEoEGDaGxsVHdLiFN3ziR/gNTUVF577TX163vuuYe9e/eGMCJxojweD/PmzcNqtQIwb948brjhhhBHJURrkZGR6nG/+/btw2w2t+ijX1hYSGpqKtu2bWvzmN4JEyYQHh7O0qVL232NHTt2qNv3Kisr2+zd35Y9e/ZgNBrV9rdz585l9OjRvP32220+x86dO7FYLMTHxzN27Ng2n7Nfv35YLBbKyspaTfkHAgGWLFlCREQEM2fObHNpIDs7m4iICNauXQvA119/jcViYfTo0dxzzz0t1vE3b95MYmIin332GT179mTNmjXs3r27zRbA4uScU8kf4IorrlBHjQ6Hg7lz58r2vy7kkUceUX859e7dm1deeUWKe0Sn9eyzz6pT8omJiTQ1NeFwOIiLi8Nms+H1enE4HGzZsqXVYyMjIxk8eDDbt29vs+mP3+9n37599OvXjxEjRpCdnc0nn3zS5oXE0Q4cOEBaWpo6Ra7VarnpppsYNGgQL774Yot4/H4/S5YsITExkVmzZrW7m2bQoEF4vV5KSkpaJf9du3ZRUFDAFVdcgV6vp6amRi32C9JoNAwbNoxly5aRl5enHhT04IMPtppFCPYFOHz4MCkpKVitVqZNmya/C06jcy75Q/MPZHAf6O7du7n77rtDHJHoiK+++oqnnnoKaJ4Wff/992V9T3Rq6enp9O3bF7vdTlVVFQaDgcOHD5Oeno7b7UZRFLxeb5uFf4BaVPf111+3+t6BAwfUqW6tVssll1xCU1MTX3311XHjKi0tbVUgaDQa+cUvfkH//v15/vnnWb9+PYqi8PXXX9PY2MjkyZOP2UcgMjISs9mMxWJpMZ0fvHiIj49nwoQJAOrSwNHHFzscDvLz83nooYfIzMzkuuuua/WatbW11NTUUFxczLBhw/j+++8xm83cc889x33fouPOyeQfERHBRx99pO5vfeutt3j77bdDHJU4lvLycn7605+qX//tb387oa1NQoTKM888A8D3339PbGwsFouFtLQ0vF4vCQkJxMbGUlBQwP79+1s9NiEhgQEDBrBhw4ZW5wNs376d8PBwdbtdTk4OQ4cOZdmyZeqyWFtqa2tpampqswumyWTil7/8JYMGDeKll17iueeeY926deTm5nZoN0FCQgLV1dUtLsrXrl1LaWkp8+bNU4tyGxoaiIuLa/HYQCDAwoULaWxsJCEhgYiICIYOHdrqNdauXYvD4SAyMpLo6GgaGxu54IILpL/HaXZOJn+A/v3788orr6hf33HHHephF6Jz8Xg8zJ07l9raWgAuvfRS7r333hBHJUTHjBs3jqysLBobG6mtrUWj0WC32zEajTQ0NDB+/HjCw8P5z3/+0+Z2uylTpuD3+1m5cqV6m8PhYN++fQwbNqzFLpdLLrkEg8HAe++9124827dvx2g0ttsUyGQyceedd5KYmMiiRYvw+XykpKS0StZtSUpKwuVyUVlZqcb5zTffkJubq862KorSqthPURQ++eQTdu/ezdVXX82oUaNwOp1t7hhYsmQJHo+HqVOnsmnTJsLDw7nzzjuPG5s4Meds8ofmRhzB9X+n08k111xzzCtmERq/+tWv1HMZMjMzeeutt2RtT3Qpv/rVr9Dr9ezdu5fw8HCqq6uJj4+nqqqK+Ph4hg8fTlVVFV9++WWrC4DU1FT69evHmjVr1CY4W7ZsweFwMG3atBb3jY+PZ8qUKXz//fftbv3bu3cvaWlpx0zme/fupbS0lIEDBxIWFobFYsFgMBz3fUZHR6PT6dRZjMWLF9PQ0MCPf/xj9T4WiwVATew2m40vv/ySb7/9lrS0NG666SZ69+5NVlYWH330UYsaBr/fz9q1a8nIyKCgoACHw8F1110no/4z4JxO/gDPPfecOrW0b98+tTOX6BzefPNNXnrpJaC5o9mnn36qbtcUoqv42c9+RlpamtoFz+fzERERgdVqpbGxkYEDB5Kdnc3q1atZtWoVfr+/xeOnTp2K2+1m5cqVBAIBNm/eTGZmJqmpqa1ea/r06aSmpjJ//vw2f5cVFxcf8+Crbdu2qRchUVFR6h7+ZcuWsW/fvnb7oyiKgsvlIj09nQMHDlBeXs769euZOHFiizirq6vR6/XEx8ezc+dOFi1aRFVVFQ6HgxtvvBGNRoPP5+PSSy8lPz+f+fPnq9sdn376aZqamrBYLOpt8+bNO/4/gDhh53zyN5lMfPrpp+pVcF5eHr///e9DHJWA5r28d9xxh/r1yy+/zJgxY0IYkRAn74YbbsBoNFJcXIzf7ycQCOD3+ykpKUGv19O7d2+ioqLYvn07y5Yta9HqNiMjg379+rF69Wr27NlDZWUl06dPb/N1DAYDc+bMoaGhgS+++KLF98rKynC5XOpJeEdSFIVvv/2WRYsWkZWVxcCBAyktLcXv95Obm0tmZiZ79+7lq6++oqSkpNVFQHD73tChQykpKeG9995Dq9Uyd+7cFverqalBURS++uor9u3bR69evbBYLCQnJzN58mSqq6uB5q6Bc+bMYdWqVdx888288sorvPLKK5hMJnw+H42Njdxyyy0y6j9DzvnkD81bxj788EN17ezPf/7zCTXMEKdfVVUVV199tfoL8M477+TGG28MbVBCnIIHHniApKQktTud3+9Hr9dTXl4ONC9pRUdHExkZSUFBAXl5eS2WIadNm4bH42H+/PlERkYe8/jefv36MXLkSJYuXUpFRYV6e/BQoUGDBrW4v9vtJi8vj1WrVtG/f3+GDx9Obm4uDQ0N2Gw2UlJSGD16NBMmTCAiIoJNmzaxaNEi9uzZg9PpBJpH9DqdjsmTJ2O1Wtm/fz9z585VK/rtdjvff/89O3fuVNfzp0+fjslkoqioiCuvvBKtVkt5eTlGo1Et+rNYLMTFxbF7925Gjx5Neno6Go2GuLg4Lr/88tP27yNa6hbJH5p7wx/Z///nP/8527dvD11A3ZjT6eSKK65QO32dd955/POf/wxxVEKcGr1ez/XXX094eDh1dXU0NjaqHQA9Hg9hYWFqL4AhQ4ZQXV3Niy++yObNm4Hm0X9aWhqFhYVMnDjxuO2s58yZQ2xsLK+99po6/b9nzx569uzZ4iS/mpoa3n33XXbs2MGYMWPUQsDevXvjcDiwWq3qfvyUlBSmTJnC+PHjiYuLIz8/ny+//JJFixaxefNmPB4PlZWV1NXV0dDQgNls5ttvv2XhwoV8+eWXHDx4UO1fMG3aNBISEli6dClxcXFMnjwZQK2H0Ol0LFmyBJ/Px/XXX0/fvn1JSUnBbrcTFhbGjTfeKC29z6Bu9cnee++9/OxnPwOaq1TnzJmjXpWLsyMQCPDTn/6U9evXA82/8D766COMRmOIIxPi1P32t79VK+KDRXRNTU3qhW5WVhaKolBdXc3o0aMpKytj0aJFrFq1CqfTic/nw2g0ttn052hms5k5c+ZQVVVFXl4ePp+P8vJyNbn7/X42bNjA22+/TX19PTNmzFC7D0LzlmidTofdbm+xH1+j0ZCWlsaECROYPXs2I0eOJCkpCa/Xi6Io/Pe//8Xv9xMeHs7+/ftxu92kp6czfvx4RowYQWRkJL169UKj0bBt2zYOHjzI3Llz0Wq1KIqibvVrbGxk3bp1jB49moKCAjQaDfv370er1ZKVlcXMmTNP87+OOFK3Sv4ajYaXX35ZbV9ZUlLCxRdfLDsAzqKHH36Yjz/+GGhuGpKXl9dmUZMQXZFWq+Wuu+4iEAjQ1NSE1WrF6/WqyT8iIoKEhATKysrQaDRkZmbicDjYvXs3L774IgUFBfTp04d169a1eSDQ0YYOHcqYMWNYvHgxS5YsQaPRMHDgQAoKCnj77bdZunQp6enpzJo1q82GWWazmYaGhnaL/MLDw+nVqxdDhw4lOjpaXda48soriYmJITMzk/PPP58xY8aQnZ1NfX09YWFhxMbG4vf7Wbx4MSkpKWrzn9raWhRFISkpiSVLluBwOEhLSyMyMpLDhw9TXV1NWFgYv/jFL2TUf4Z1u083PDyczz//XO0R/f3333PNNdd06LxrcWpefvll/v73vwOg0+n48MMP5XhOcc65/fbb6dWrF2FhYepo/vDhw+qWtp49e6IoCocOHSIjIwO3283AgQNpampCURRSU1Ox2+0drku6/PLLSU5O5j//+Q9ut5v33nuP999/H6fTyYwZMxg2bBg6na7V41wuF/Hx8bjd7hZ1A22prq4mEAiwbt06kpOTufHGG0lKSuL7779vcb/a2lri4uLQarWsXbuWkpKSFmdzlJaWYjQaMRgMrFmzhszMTHQ6HdnZ2Wzbtg29Xs/IkSOlwddZ0O2SPzTvq128eLG6zrVs2TJuvfVWOQL4DPryyy9bNOp44YUXuOiii0IYkRBnzssvv9yiSr2+vl4d/ZvNZnX036NHD3w+H9u2bSM+Pp4rr7ySiIgITCYTy5YtY8GCBWzfvp3i4mIaGxvV31HBbXfV1dUUFhaSmZlJdXU1paWl7Nu3j/79+zNt2rQ2m+gEVVZWkpaWhlarpaCg4Jjvp6amhvz8fOx2OzfffDNarZYRI0aoLYiDMdlsNhISEnC5XCxbtozevXu36OIX7HuwdOlS6urq6Nu3LwMGDODbb7+ltraWiIgIacd+lnTbPRT9+vVj4cKFzJw5E7fbzfz588nMzOTPf/5zqEM756xatYprrrlGLUp64IEH+MUvfhHiqIQ4c8aNG8e4ceNYv349Xq8Xt9utbnuD5rX/uro6dVtcWVkZM2fOJCUlhZSUFHr37s0333zD9u3bqayspLKyEq1WS3Z2Nnq9Hp/P12I7oU6nY+DAgepOgo4cZlZTU0NsbCxJSUkcOnSIKVOmtHvf7du3U1JSwo9//GPS09MBmDx5MsuXL2fDhg3Mnj0bi8VCIBBQk3tNTU2LRB4IBGhoaCArK4tVq1aRnJxMv379yMnJ4Y9//CNarZYrrriCrKysU/z0RUd0y5F/0KRJk3j33XfVbnJ/+ctf+Otf/xriqM4tGzdu5NJLL1X7ll977bU8+eSTIY5KiDPvqaeeIjY2ltjYWAKBAAUFBXi9XqC53iUhIYEDBw6oo/iePXuqj42IiGD48OEkJCQwcOBAdZdAVlYW6enp9OzZkwEDBjBmzBjOP/98MjMzyc7Opn///rjd7jbPEThafX09CQkJ5OTkUFRU1O5pgbW1tWzZsoUePXpw/vnnq7fHxcWRmZnJli1bCAQClJeXYzAY0Ol0rFq1irFjx7Z4T5WVlWoRYGlpKeeffz5jx47lgw8+oLa2FoPBwG233XayH7c4Qd06+QNcddVVPPfcc+rXv/3tb3n66adDGNG5Y+fOnVx44YVq5fLFF1/MggULpJBHdAvp6en87Gc/Q6fTERsbi9VqJS8vj5qaGkpLS7FarbhcLuLi4tQtgUfKyMggOjqa/fv307t3b7xeL2FhYfTu3ZucnBwyMjLUx9bU1JCYmMjQoUNJTk5m9+7dx9wx4HQ6cbvd6sWFw+GgsLCw1f08Hg8LFizA7Xar0/1Hmjp1KqWlpezfv1+dSVi0aBEej6dFy19oLrB2Op2sWLGCYcOGMWvWLNxuNwsXLiQQCPDoo48SERFxCp+4OBHyWxi46667Woz477//fl588cUQRtT15efnc/7556tdwaZOncrHH38sW/pEt3LrrbfSs2dPMjIy8Pl8FBUVsWXLFg4ePIhWq1V78Pv9foqLi1s8VqPRkJubi9vtxu12A6h1A0eyWq243W6Sk5PR6XRMmDABh8PBsmXL1McdraKiAr1eT1JSEr1790ar1ZKfn9/qfnl5eRQUFDB58uQWo/ig0aNHYzQaWbt2LfX19bhcLjZv3szFF19MTExMi/tWVlaybds2PB4Pd999N7Gxsbz33nvU1tYSGxvLxRdf3OHPVZw6Sf7/85vf/IY//vGP6td33nknb7zxRugC6sL27NnD1KlTqaqqAmDs2LF88cUXmEymEEcmxNkVERHB7bffrrbcDRbpjR49mrFjxzJ06FC1MLCtniOxsbGkpKRQWlpKZGQkZWVlre5TUlJCWFiYumV24MCBmEwm6urq+Pbbb9WlhiNVV1cTFRWF2WxGq9WSkZHBwYMHW9xn3bp1bNq0iQEDBjBo0KA22+xqtVomTpzI1q1baWhoYOPGjURHRzNnzpwW93M4HOzfv5/CwkKuvfZacnJyqKio4PPPP8dqtfLqq6/KjOBZJp/2EX7/+9/z29/+Vv36lltu4fnnnw9hRF3Ptm3bmDp1qrp1aMiQIXz11VdERUWFODIhQuOyyy5jyJAh6HQ6wsLCqKmpYe3atfj9fsLCwkhLS8NoNFJRUYHD4Wj1+NzcXAwGA4FAgMrKyhbJXFEUqqqqSEpKUrfzmc1m4uPjMRgMeL3eVhcAiqJQX1/f4gCtgQMHUllZqZ7Id+DAARYvXky/fv3Izc095mFb559/Pna7nbVr11JZWclNN93U4kJBURQ+++wz9u7dS1JSEjfddBMAr776KvX19fTt27dVO2Jx5knyP4JGo+HPf/4z999/v3rbPffcw2OPPSbbADtgw4YNzJgxg9raWgBGjRrFihUr1C2VQnRHWq2W+++/n7CwMCIiItDr9RQUFLB+/XoURSErK4vU1FQaGho4fPhwq8cbjUZ69+5NeHg4jY2NLab+g2cIBCvwgzIyMqitrWXo0KG43W5Wr16t9jJpbGzE7/eTlJSk3n/o0KF4vV52795NeXk5H374ITExMVx22WUoinLM5G8ymUhNTaWyspKcnJwWW/sCgQArV66koKCA2tpa7rrrLvR6Pdu3b2fNmjVoNBo++OCDk/5sxcmT5H8UjUbDU089xe9+9zv1tj/84Q/cf//9chTwMaxcuZJZs2bR0NAAwMSJE1m+fDkJCQmhDUyITqB///7qHn6NRkNYWBj79+9XG9sET+Frr0o/NTWV7OxsmpqaWkzPHz58GLPZ3CKRQ/Nsgd1ux+PxMGLECLxeLytWrKCpqYmysjKMRmOLxwR3H2zdupX//Oc/aDQa7rzzTurq6jAajcdM/oFAQC0gNJvN6u9Jj8fDkiVLqKysZP/+/eTk5HDeeefh9/t59tlncTgcXH311a1iF2eHJP82aDQaHn/88RYHAT3zzDP8/Oc/l06AbXjnnXeYPXu2Wl08Y8YMli5d2qrgR4ju7Je//CW5ubnodDr0ej3R0dHs3LmTHTt2kJ6eTnJyMoWFhW3+jtFoNAwYMIDIyEh2794NNJ/UV19f32rUD83JPxAIcOjQIRISEhg9ejQ6nY4VK1ZQWFhIQkICBoOhxWN69uzJ7t27aWho4O677yY6Olo9hOdYx+ouW7aM0tJSZs2axb59+1i/fj11dXXk5eXhdrupqqrCYrGoTb7eeecdDh06RFhYmByvHkKS/I/h/vvv54033lALUebPn88FF1ygrot1d4qi8Kc//Ykf//jH6pripZdeSl5eXotTxYQQza3Ff/Ob3xAdHY3VaiUiIoLk5GS2bdvGzp07GTlyJE6nk40bN7b7+IEDB1JbW8uuXbsoLCzEYDC02RRHr9eTmJioLiPExMQwbtw4zGYztbW1NDY2tpjJtFgs5Ofn09DQwJQpU0hKSsLv92Oz2Y45Mq+vr+fLL78kJSWFRx55hB49evDmm2/yySefYDabGTBgABs2bGDIkCEMGzaM0tJSPv74YzweDy+//HKLA4XE2SXJ/zhuuukmPvroI8LCwoDm6e3x48dz4MCBEEcWWk6nkxtvvJFHH31Uve3222/nv//9r1T1C3GUYCOxSZMmcfXVV6PRaKirqyM2NpaePXuybds2GhoaMJlMHDhwAKfT2ebzjBkzBq1Wy5YtWygqKiI1NVX93XS0nJwcysvL1SLC8PBw0tPTiY2Nxel0smTJEmpra6moqODtt9/G4/HQr18/td9AsClPcnJym8+vKAoffvgh9fX1zJ07F7vdzoABA6ioqGDbtm0MHDiQRYsW0dTUxE9/+lMCgQB/+tOfqKysZO7cuephPyI0JPl3wFVXXcXKlSvVH4L8/HzGjRtHXl5eiCMLjeLiYiZPnsz8+fPV25588kleeumlY04PCiGaT7bMyMigsbGRxsZGsrOz6du3L7t378ZgMFBfX8+OHTvU+x9ZbBwZGUlKSgoNDQ3YbLZjtsIdOHAgbre7RY1AVVUVycnJTJw4EYPBwKeffsrTTz9NU1MTd999NxMnTqSgoICGhgbKy8sxmUztFuyuXLmSXbt2MXz4cJqamliyZAkmk4lHHnkEaK6VWrlyJUOHDiUQCHDfffexceNGkpOTeeyxx071YxSnSJJ/B40fP56NGzcyePBgABoaGrjssst45JFH8Pv9IY7u7Fm+fDmjRo1iy5YtQPM+5g8//JCHHnpIHd0IIdoXERHBs88+i8FgoLKykuLiYkaMGMGoUaPw+/243W6KioqoqKjA6XRSXllOSXkJVTVVNDQ0kJSUhMViwWAwHHMGMiEhgYiICDX5+3w+GhsbSUlJUQv4ggf69OvXj507d5Keno7b7Wbbtm3U1NSQnJzc5s91UVERn332GUajUW0uNGTIEGbPns3YsWN56KGHqK2tpby8nH379vHkk0+yZcsWwsLCWLt2rezp7wRkmHYCevbsydq1a7npppv45JNPgObzANatW6ceDHSu8nq9PProo/ztb39TRyI5OTl89tlnDBkyJMTRCdF5KYqCoigtkuj48eOZPn06ixcvpq6ujn379jF8+HDi4uKYP38+hw8fZvXq1YwYOwKdWYfOqKPJ14TNbcOn8eFyu9DoNBSXFKPVacntnYter2/xB6BXr15q3/7y8nK0Wi0REREsWLCAgwcPMmbMGK644grKysooLS2loKAAp9NJXl4eAwcOJCIigr179wLN1ftNTU3U1tayZMkS7HY7F198MQkJCVx22WUtuncuWbKEhIQELrzwQuLi4li9ejVNTU188sknkvg7CUn+Jyg6OpqPPvqIp59+moceegi/38+KFSsYMmQIL774Itddd12oQzztCgoKuP7669m0aZN620UXXcQ777xDXFxcCCMTonMLBALqgTlHj6Bfe+01cnNzqaysJCIigoqKCjIzMxk/fjw7duzgQP4BrE1WJl8yWe1577A3r9+bIk148JCWlsah4kNgau4GqFW0aNGi0+gIM4TRo0cPdu7cyb59+9RTBN977z18Ph/XXnstI0eOBJp3B/Tu3Rur1YqiKCxevJjc3FyamprU5K/VagkPD2fnzp3qYCA/P58+ffq0SPybN29m06ZNTJgwgdTUVIqLi6mvr+eOO+4gOzv7TH/kooPkEuwkaDQa7r//flasWKGO9hsaGrj++uv50Y9+pLa17ep8Ph9PPfUUQ4YMURO/wWDg73//O3l5eZL4hWiHoij4fD51F4zRaGw14tXpdHz88cfo9XpKSkrYv38/9fX1pGWmYYwwktYjjerKahZ/tJhNqzZRb6nn0J5DRERGkN03m8qySjL7ZRKbGEtJYQkBfYDwhHB0MTr8EX7sWjvGBCPegJeFeQtZ9vUyvt/xPbFxsdx666306dMHp9OJz+dTZyZiYmK49NJL0Wq1OJ1OrrrqKq688kr1j0ajobq6mltuuUXt4ZGWlqa+p4aGBj766CO1cZHFYmHnzp306tVL7ewnOgdJ/qdg8uTJ7Nixg+uvv1697cMPP6R///688sorXbop0LZt2xg/fjwPPvigehxvnz59WLduHQ888IBM3QnRjmDi9/v96HQ6DAZDu/Uwo0aNUnv/FxYWsm3HNgxxBmITYzGajEyYNgGTycShgkPkvZPHgd0HCBAgLSsNe5Od6vJqsgdmEx4Rzp4te3A5XOiNerR6LbU1tezYugO73c6hg4dQFIU5c+dw0Y8uwm10U2WtoryunJKqEkoqSqiqrqK+vl6tCyguLqahoQGdTodOp2Pbtm0sW7aMiRMnMmPGDIqKioiKilLrBwKBAAsWLMBms3HVVVdRX1/Pvn37cLvd/POf/5TfGZ2MRpG+tafF+++/z5133tmiB8C4ceP45z//ycSJE0MY2Ympqqrid7/7HW+88Ya6tq/RaLjnnnv405/+RGRkZIgjFKLzOnKaX6/XdyjhVVdXc9kVl1GQX0BycjLDJgyjydXE3i17mXj+RCylFmwNtuYjgD0uvD4vWq0WW4ONxMREsnKzQAOWCgsejwdTpAm7zY7X60Vv1GPUGSktLuX8C85n9tzZaLQ/XIgofgW/30/AF8Dv86P4FcqLyjlccJjt27YzfcZ0LrjgAirKKnjnnXdISUnht7/9LXq9nk8//ZS+ffsyYsQIAJYuXcpHH33ELbfcwt69e6mpqWHfvn38/ve/Z9q0aWfk8xYnT9b8T5N58+Yxc+ZMHnjgAXUL3IYNG5g0aRJXXnklTzzxBP369Tstr+X1etmxYweNjY3ExMQwdOjQVt26TlRjYyPPP/88f/vb37DZbOrtgwYN4vXXX2f8+PGnGrYQ5yxFaU6ifr8frVaLXq8/7u4XRVHIy8tjzY41DLx2IPbP7dTsq2Hn+p30GdYHn8/Hge8PEB0ZjRJQyOyZyfDJw3HYHZQdLmPTt5uos9RhKDegBBQC/gAOmwO3x03/of3pldsLg8aAzWZj4YcLsTlsLRI/gEanQa/TwxEnbTfuaCQjOwOX4mLr91vp2b8nCz9aiFanZe4NcymvKaemqgaHw4HJZMJms3H48GEWLlzIyJEjqaurw2azsWfPHq644gpJ/J2UjPzPgBUrVnDnnXeqhTLQXCwzd+5cHn74YYYPH35Sz1tbW8uzzz7La6+91qKuICUlhVtvvZV77733mD2429LQ0MDzzz/PP//5T7UvPzQXNv7+97/n7rvvblHMI4RoKTjaVxRFHe0fL/E7nU6+Xv41L372IlaPFcWvoNPpKFhfgLfeS2paKi63C6fDyaixowgzh2FvsJM9IJvEtOaf8ZqqGlZ8sYLpF00nu282AC6Hi8JdhbgcLtIy0oiMjaS6oprd23eDFm657xbCTG03BQJwu9xs/Hojg0YMwhxn5tk/P4sp3ERkTCT3PXIfUdFR+Lw+vlvyHRo0DBs/DK/Ly79f+Tdut5uZM2diqbWwadMmoqOjeeKJJ0hKSiImJkY9dVB0DpL8zxCfz8dbb73F73//eyorK1t874ILLuCOO+7gkksu6XBTnH379jF79mxKSkravU9WVhZLliyhf//+x32+Xbt28cILL7BgwYIWx4jqdDpuvvlmHn/88XY7ewkhmkfuwcSv0Wg6PM1fVlZG3td57LLvIn1sOhqjhtqKWuqr67FUWdg4fyPeGi9JSUnUN9TTO7c3uQNyqauuw+Vw0XdYX6ITo9HpdHz+zuekpacx/dLpakyWMgslBSV4vB56DexF+aFyklKTWLV8FbMvm83w8cPbja1ofxGVhyuZNHsSVquVZx57hsaGRh7752P0HdQXn8dHTUkNW9ZtYcCwAfQa1Iv5L81n3659TJ8xHVO4ibVr1rKvaB+zfjKLKGMUEdoIzHozqXGppCekEx8fT1xcHHFxcXJREEKS/M+wpqYmnnvuOZ5++mlqampafC89PZ2f/exnXHPNNYwYMaLd0UJtbS0jR478IfHrgEuBAcBeIA/4X5+hHj16sHXr1jZnAKqqqvjwww957733WLduXYvv6XQ6fvKTn/DII4+Qm5t7Su9ZiHNdsKgvEAioBXHHG+0HAgG2bt3KovWLqIuto8/EPhgjWs+q+Xw+XrrxJeoO1IECkdGRjJ82HgJQXVyNz+ejR04PjEYj+QfyqSip4OKrLyYyOhJ7vZ2AEiA8Mpy6yjqqSqrQ6XRMmzON/777XyJMEVx363Wtpv+DNny9gcSkROLT4/ns3c9wuV14XB4GDxvMj376I2x1NspLy6mvq2fSBZNYunApy79aztjxYxkydAjLly5nZ/5ObnjuBtL6pOF1e3E0Omiqb8JpdeJqdIEN9G59i4uC5JhkrFYrQ4cOJTU1VS4KzoIOJ/8mms50LOc0p9PJ/PnzefbZZyk+XNzq+1k9s7j00kuZMmUKkyZNarGN7rFHH+Nvf/pb8xfDgf8C2Uc8uAi4Etje/OVvHv0Njz72KD6fj+3bt7N8+XK+/vrr5vPDAy3/uc2RZq6//nruvvtucnJyTtfb7ZbMyGFG3cHR0/wdSVJ2u52lXy9l7eG1mAaa6DG4xzEvFgKBAM/OexbLQQsEYMT4EQwZNwRXk4tDuw6BBrL7Z+N0Ovnmi28YMHgAPXv2RKPVYAwzYgwzomgUDnx/AGOYEXO0GW24lu83fs+Pfv4jMrIzWr2m1WJlx7odRMdHs37NegxhBm67/zaK8ov46O2PmDptKuedfx47N+8kMTmRyqpKPn33U4YMHcJlV1/G4i8W892G75h21zTGXDHmmJ9H8KLA0eDAUm5h17Jd+AN+BvQdQKI5kQh9BKmxrWcKYmNj5aLgNOlw8v8jfzzDoXQPgUCAwsJCtmzZwv79+1slYwA0kJSU1NyGMz6R9XPX46pzNY/4C2iZ+IOKgFzAD4Y4A8lPJFNVW4XP62szjqTkJEaNGsXw4cPbPRhEnBj5GTm3nUxRHzS3ws1bnsd+736yJmYRk9yxo679fj/P/OgZqvdVE2mOZPbVs4lPjqfJ2sThvYcJM4XRb1Q/lv93Oa4mF9MvnU5UTBQBfwCfx0dZYRlel5e0HmlYqizYm+zs2LaDISOHcMk1l6AP02MIM6izADvW7WDfjn1U1VaRmpHKz375M8LDwmmoaOCLT77g8OHDzL50Nn6Xn7q6OlZ9s4q+/fryi1//go/mf8Tqb1fTc0pPrnn0mg5/pnUldXz96tf4DD4mz5tMWs809aLA0ejAZXWBFXRu3Q8zBXJRcFpI8g8hu93Ovn372Lt3L4cOHWr7QqAceO1/f78c+OwYT3g5sPB/f78NSGv57fiEeAYOHMiQIUNkPf8MkJ+Rc5eiKHi9XhRF6fA0v9/vZ8OGDSzZsgRrkpXcCbkYwk5sV47P4+PZec9S/H0xqampTLpwEmk90rDV2yjeXwwKmCJMbN+2nRkXzaD3wN4ANFmbOLDtAD1ze5LcIxmP20N1cTXrVq+jpqqGaTOnkd07G3OkGZ1OR2NjI4s+W4TNZmPSjElcecOVBHwBGioaUDQKkQmRLHhtAbu37CY9PR2LxUJu/1xuuvsm3nn1HdasXkPGmAx+/tzPO/zeCjcX8t1H3xGeGs7MG2YSl9x+0zCfx6deFDQ1NqnLBzrXDxcFKTEpZCRmqBcEGRkZamdE0Zok/07C6XRy+PBhioqKKCoqorq6uvli4BAQPDzvYeCJYzzJw8CT//v7TyFuVBxpaWnk5OTQu3dvYmNjz+A7EPIzcm7y+/0nXNRXUVHB62++TqmmlJQJKWQOOPlzP1x2F09f+zT1RfVEx0STOyiX3AG5NFY2UldTR0RUBCWlJUSaI7no2otAgd0bdxMeFs7g8YNbjIibrE38+7l/k9kjk145vVA0CnU1dezbsw+vx8vl11zOoCGD8Lq9NNmb8Pl8uD1u7DY7TqeTNSvWUFVdhTnKTL+B/bDUWqisqaTH2B7c8OQNHX5PmxduZveq3SQNTmLGj2YQHhF+Up9NWxcFrioXSfokZgyewYwZM07qebsD2effSZhMJvr3769W6vt8Purq6ti/cj8r5q9ovtPeYzzBUd//6e0/pdfEXmcmWCG6gSOL+k5kmj8/P59X332VDYc24Pf52bNnD+ZYM9HJ0cSmxhKfEU9Cj4QOT/+HR4Zz7/v38vTcp3HXutm3fR+HDxwmMzuTnn17Yim3EGGKoKqiiuL8YgLeAPih14BeLRJ/QAngw0fvIb05fOAwkbGRlBeXU1dbR1xcHGOmj0GDhu83f9/iPYeFhREbE0vhgUK8Pi/DRw6n/6D+bPhuAzUNNYy5YQxTb5zaoffi8/hY8dYKyg+W02dmH8ZfOP6UOv/pjXqik6KJTooGoLaklipLFYOSB0lvkuOQgr9Ozuv10q9HP6qrqju85p+SmsK+4n2n3PhHnBgp+Dt3nMzefa/Xy5o1a1i+cznODCep/VKpr6nHUm2hvqoea42Vpuom/C4/+Jt32ETGRhKTEkNsWiwJGQkk9kwkIuaHqepAIIDL5UKj0VBbXMvz1z6P2WDGHGUmQAC9Xk9CUgJatBw6eIi4uDgGDh5ITv8c0no1r/spKFjqLNTW1mKptlBRXMHebXvR6/Vk9cmiX/9+xEXGMWzsMJxWJz6vD1O0iej4aMLN4RjDjHy64FNWL1vNsFHDuPSaS/nk3U/4fvf3mDPNxCTFoFE0RMREEJUYRWxKLPGZ8SRkJhCbFqsmd3udnWWvLMPusDP6itEMGD3gtP6ble4pxbHTweyBs5kxfUaHt1F3Vx3+dOQXW4gY4LZbb+NPf/pT83a+K2m/2v9/2/1uu/U2Yg2xZzVMIc4FR+/dNxqNHRrt19XVsWjZIjbXbCZxVCJZvbMAiEmMIXtAtnq/QCCA1WJV9/XXV9VTV11HSWEJikdpLtg1GoiMiyQqKQpzopnk7GQCvgAbPtlAn/P7ULKheQ9/UlISkQmRVJZW4rA58Lg8lJWUgQKKTqH4cDEBf4C6ujrqLfXYGm143B60Oi2xSbF43V76D+qPPqAnJj4Gd5ObyJhIYpJjCItoLgK22+x8PP9jNny7gTHjxzBq4igWvLUAu87Oza/fTERCBJZKC5aqHy5wCnYX4NvoAz9o0GCOMeP3+ik/UI45w8zU66aSO/L0bScOBAIc3HiQ8OJwrp1wLWPGjOnQv1l3J/v8u4A29/lfwg/7/L9ETfxZWVls2bLlhDv9CdHdnczefYA9e/aQtzqPEkMJvc/r3WLk3lE+n4/G2kb1oqC2vBZbtQ1XvQtHrYPyg+XEpcfRI7cH8RnxrP9oPbZyGykpKWT0yMDrbV6jLyosQqPREBkZSXRcNBqthoASwGQ2ERsfS0q/FJIGJKEN17Jq/ipcFS4mTpjIwCED0Zl0xKfEk5jc/Lsjf3c+iz9bTHFhMUNHDEVn0LG/cD9Jw5O44JcXtNmjIMjeaKe2vPm97Px6JxUHK/BqvaSnpqNDh1ajxRxzxFJIejwJWR1fClE/N4+PA98eINWaypUzrjxtLdS7A0n+XcTp7vAnhPjByRzI43a7WblqJSv2riDQK0DOqBy0ulM7uS4QCPzQZjsA699bT9nBMsJ6hNGjVw/s9Xbs1XacDU4shyxU7a0iNjKWzKxMBg4fiFav5eu8r0mMTySnbw46o464tDjCzeEoyQqEg6JVQAN1B+pY8dYKevbsycVXX4w5rrnyPyE+gRWLVrDr+1343D7SM9Kpqa/Ba/Jy3k3n0Xd83w6/l3Xvr6NgawEZozOYdvU0mqxN1FXWUV9dT0NNA9YaK/YqOwF3c52CTqtrro9Iar4oSMhMIL5HPNGJ0a2e32V3kb8in77avlx90dWkp6ef0mff3Ujy70Jqa2t57rnneO2111q0DE5NTeXWW2/lnnvukRG/ECfgZPfuV1VVkbc0j+0N20kbn0Zij1P/ufP5fHg8HgwGA7XFtax8ayUOr4MhFw4hd1jzNLlOp0Ov16P4FcqKyqgtqWVH3g6qdlYRHR5Nj6weaHQaDuw+QK9evUhITMAf8BMWFUZUdhSR2ZHow/U4a5xUr6/GZDax5fstJMYlMmLUCCx1Fgr3FWK32TEYDNhtdgKmAGN+NIYJcyegN3Zspdhld/H1q19TV1PHkAuHMHLqyHbvG1wKUZcPquux1dhoqm364aLgqPqIiJgI3GVuRieM5oqLr5CdTCdBkn8X5PV62blzJw0NDcTGxjJkyBAp7hPiBJ1MUZ+iKKxZs4ZV36+iOqqa3PNyCTef3Da1I7lcLjWO/Wv2syVvC+Gp4Uz50RT1IJ/g67tcLhoaGggPD1eL2horGtn4wUZKtpagD+jxury4nW6yc7PJyspqvrBwe1AUpfkYX6+f6LhoIlIjKCkuYfeG3SgeBY1WQ3R0NCaziXp7PXG945j35DzCI8LR6XQd+owsZRaWv7oct9bNedee16Lm4UQEAgEaaxupq6rDUmmhoaYBW40Ne5Udk9vEFROv4JabbyE8/NQ//+5Ikr8Qols52QN5nE4n737wLh9+8yF2v53o+GhiUmKIy4hrs1K/I4LV/Hq9Hr/Xz3fvfUfx3mLShqcx+YrJGMNbrqv7fD6ampqIjo5ukYSDvQiqi6rZsXgHhzcfpupgFYpXIS4mjvj0ePQ6PQFXAC1aNGiwOWxYbVZsTTYcHgeeJg8BAoRHhzNq1iim3jSV9L7pLT6zQCCgvm4g0Lzb4MgWx0Xbiljz3hrCUsOYecNM4lPiT+jzOJ7iHcW497gZ32M8l19+uVT0nwJJ/kKIbuNki/rKysr4YtkX7GrahaGHgSZbE/XV9VirrTTVNKmV+sYwI5HxkcSkxjQXsWUmkJCV0CqJQ3Midzgc+Hw+bDU21i5Yi8PjYOgFQxl23rBWFyROpxNFUTrUtc7v9/PaP15j78q9BIoDGGOMaD1aFL+CEqvgH+5HyVDQpmqbO4FWgvKlAk5IiEigV49e6vsxx5l/2I6YmUBCZgKKrrnjodlsxu/3oygKOxbvYM+3e0jon8CMeTMwR5lPaQ//kQL+APnr84ksj+TySZczcmT7ywiiYyT5CyG6hZM5kCcQCLB582YWb1yMJc5C7sRcjKbWo/Fgpb6l0kJDdQO2ahtOixN8oPgUIqIiiEyMJC41jvjMeKJToolMjiQ8PJzCTYVs+O8GDAkGzpt7HglpCXg8HgKBANB8wdLU1ERUVBRms7lDbYXtdjv79+/nk08+IeAI4G30ovRW0F+mRzdC17w7yAMEIOAOoHymoNvf/HlcdeVV5GbnUldRR0NtA43VjdiqbTgsDjR+DV63t3n3QFIsMakxRCdGU7ChAGuDlZzJOUy8ZGKLmQKn06nGHbzgOpGLAq/Ly/7V+8l0ZHLVrKvk1NHTRJK/EOKcdrJFfXa7ncXLFvNd8XeYB5nJHJR5QvvHPW4PdZV11FXUYamyNCfRKhvOBieagAZNQIOlzILf7yeuVxwTLp9AWp+0FpXtwUQeGRmJz+dTL16Cv7b1ej0Gg0Gd/na73Xi9XiIjI/F6vfzxV3/EvteOJk6D4R4D2qktk27AEUBzQIPmPQ2KomAymbjvvvtaXBipRYYBhdJDpTQ1NGGrs2GttWIpslC5v5ImRxNpWWkkJCcQlRhFTEoMMakxhMWGkdEnQ61JCl4QKIqifpbBi4K2/l2cVicFKwoYYBjA1ZdcTUpKSoc/f3FskvyFEOesk53mLyoq4ovlX3DAe4Cek3qq7WNPhc/no76+HsWvUHWwinXvr6PR0UhYfBgx4THNle2+/1W2x0USERdBVHIUGbkZJGQlEB7ZurAtuNbv9XppampCo9FgMpnQ6XTsWrKLlZ+upNxXjiHdgNaghZHAWFDiFJQSBc1ODZrtP3weF1xwQat++MEiw/r6eszmH6byLcUW1r+7Hn+En4FTB6LX6Zsb/dRZsVZacTW6MGgMaDVaIqKa30tsSixxGXEk9kgkOvmHz7SpqYlAIEB4eLj672OrsVGxvoJxSeO44pIriI4+9X8D8QNJ/kKIc9LJHMjj9/tZv349S7YuwZ5sp/f43id8El9bPB4Pfr8fnU5H4bZC1n+wHiVKYezlY0nLTkOj0eBuctNQ3UB9dT1VJVU4LA48DR4Ub3OFfrgpnMj4SGJTYonN+F8L3YwEdAYdVqsVs9mMXq/HZXex4s0VVJVV0WtiLwothezZs0dNqkePuoNGDB/BvOvmtRm72+0mMjJSvf+BdQfY9NkmTJkmJl41kciYSPW5PR5PcyGgVt+i+5+txoatxkbA9b+LnP/t6Q+LCSM+PZ6U7BTis+KJjI2kqrCK+i31nNfjPGZMm6F2WgwuJ0RGRnZ4Bke0TZK/EOKccrLT/A0NDXy17Cs2VmwkZlgM6f1OvWlMcNQcvPDY8vkW9m/YT3zfeKbOnYo5yqzez+124/F4sNlsmM1mdZbCXm+nsaaR+qrmxjjBJj8anwbFr6AP05OQkUBcahxavZbdq3ajj9Yz/qrx5AzOAWD58uWsXr0ap9OpXoQEf/WHh4czefJkzj///NbT7kcVGQYCATZ9uon8zfmkDU9jylVTMBh/uDiy2+1A8+yF3+9v8TkYDAaMRiP2BrvaybCyuBKP1YOzzqnu6dcoGnqn9eZnl/yMSZMmqZ9dIBCgqqpK7WUSfH6NRqNe4B25BCKOTZK/EOKccTJ79wEqKytZ8OkC9jr2kjo4leReyZiiTac0svT7/bhcLgwGA06rk5X/Xoml2kLfqX0Zc37r/vNtjbD9fr86a9DiffoC1JTXUF9Vj7PRSWNNI1X7q6jIr8AQYSA1PZXYpNjm9rn/OzRIH62nqKyIktIS3C43YeFh9O7dmyFDhgC0qidwOBxERkZiNjdfoHgcHla8tYKa8hoGzBzAqBmj1HgURcFut2MymdpMvsELsmAhY7CWITo6GqPRiMFgwFJpYeuXW0l2J3PZpMu44IILWnw2dXV1pKSktDuDE7zg8/v9eL1ekpKSTvSfrFuR5C+E6PJOdu9+UF1dHXlf5tHoaaTR1Yjdb8eldaFEKhhjmre7RcRGYI41t6r2b4vH48FqtaLT6SjfX86WT7aAGSZePZGe/Xu2un9TUxNarRaTydSh91pfX4+iKISFheH3+9n2+TYOfX+IuH5xDBo3CHuDnYaq/7XPrbbjcXjQoSMsLIzIuP91ykv/YevekX36FUXBarViMplQlOYtfQ2VDaxdsBaX4mLclePoM7SPWhQYCASw2Wyteg+058heBcGv7Y12Dq45SKYjk4smX0SvXr0IDw8nPDwcl8tFU1NTh5K5oig4nU6io6M7tJujO5PkL4To0k62qK89TqcTi8Wi/imvKaestgyb10ZToAmPwYMmWkN4bDiRcZGYY5svDLQ6rTrNH6xg3/bVNvas3ENkdiQTr5iIKeqH5B68j9vtVtfrjyeYaCMjI9HpdDgaHax8ayX1tfX0n9GfwZMGtxjB+/1+nE4nWr8Wm8X2w1bEmpZbEU1mE5EJkUQnRROeEE6Pfj2IS49Dr9dTvLOY7977Dn2inmnXTWs+EdDrVUfybrebqKgoDAYDBoPhmBddR+5GCGpqaOLQ6kMMDh/MFRdeQWJiohp3dXU1Xq+XuLg4oHl3Q0RERJtd/YINk2JiYlrEEFzmEC1J8hdCdFkncyDPyQiOhuvq6rBYLNTV1VFaW0plQyVN/iYcAQeBiADecC/RCdEYI4xszduKpcpCr0m9GH/R+FYJyOPx0NjYqI6wg3Q6HUajsdXFwNHLAlUHq1i9YDWBsAATrppAVr+sFvcPJlqTyaTuCDjy/aCAvd5OQ3UDlioLlnIL1morilNR196tVVYcVgfxufFMmDOB9L7papX+kfUAwQswr9erbuUD1GORDQYDTqdT3Y0QVF9RT8V3FYxLGcelF1yqLjFA82yM0WgkKipKvc3r9eJ0OnG73S3ei8FgIDw8nJiYGJYuXcqYMWOIi4tTLwgBXnrpJTweDz179uSKK644oX//c5EkfyFEl3OyRX2nm9frpb6+npKSEmpra2m0NVJaV8qeA3soqy0jvmc8cdlxGKIN6gxBRGwEvkDzTMWRye7I9+Z2u9WLGmheFjAYDMTExKDT6dj77V62fbkNcw8z06+bTnR8y21wDoejVaI9WvAgoUAgQFNTEzqdrvlCweOjobKB1fNXY6mzoInVkBiV+EOVvk6HIcJAfFo8iZmJxGXGkZCZ0GZr42D1f319vXoRAM0XanVFdTh2OZieO51ZM2a1OJ+ksrKS6OjoDnUz9Hq9eDwe4uPj+eabb5g1axb79u2jb98fTh+84IILsFqtjBs3jgULFvD444/zy1/+ssXOh+5Gkr8Qoks52aK+MyFY6OZyuVqMRhsbG9W96w0NDVTWVVJuKcfqtVJrr0UXrcOQYMAUa1IvCkzRplYzF4qiYLPZCA8PR6vV4nQ6Wf/Bekr3lZI2PI0Jl04g3BTeYiuc3W4nLCwMo/H4tQlHF+opikJDbQMrX1tJo62RwbMH0290P3Q6HU6bk8baRsqKynA2OnHUOWiqPaq1cUJzPUFcevMFQWx6LC6PS12mCL7mwc0H4QBM7T+VUaNGqbHr9XpsNhvp6ekdOqzM4/Gg0+nUiwSn08nYsWOZNWsW//znP9FoNNx9990cOnSIvLw8APLy8vjpT3/Kzp07ycjI6PC/9blG9kQIIbqEo4v6jre+fKb5/X6sVivh4eGtGtAkJSXhdrvV3v2DGYzL5aK4uJjIyMjmpjkN9ZTWllJTWEOtvxYHDpRIBV108/738OhwFL1CYmpi85Y/i52Vb6zEarMy+qrRDJk4RC3IczgcaqOfYDfA4IzIseIPVtwHL55qi2tZ+eZKAqYA5996Phk5zckxWEPg8rkYPmW4mqy1Wi1N9c3nHNRX12OttVJZUUnh7kLwgtftJSY+hqjEKGJTY4lNjcVtd5PWlMacC+YwcOBANR6Px0N5eTnR0dE0NDSot2u1WsLCwlqcYgjNyxpGo5Hw8HCsVivR0dEYDAZGjRrFhg0b1P8v0dHR3HjjjUDzxcHUqVPJzc3F5XKd6n+BLk1G/kKITu90F/WdKpfLhcvl6lB1PoDVasXtdhMfH6+uWQe373k8HpqamnA4HDQ1NVFdV83B8oPUNdWBCTx6D26tmz1r96CJ0jDm4jHkDM1BZ/ihhuDoQrrgdPvR6/zBorzg+vyRhXf56/PZ/NlmTJkmZlw/o8VSgsfjwePxtLg/oD7PkVsRNRoNziYnlioLXoeX+qp6GmsaaSxrBBf0i+zH//36/+jRo4f6GIfDgc1ma7N9byAQwO1243K5WhQzpqamYjQaue666+jVqxe33347PXv25Pvvv2fs2LG8+eab3HDDDdjtdhRFaVE7MGbMGJ5++mkmTZqkXsh0t+l/GfkLITq1kzmQ50yqrKzE5/OpFejHU11djclkUreqRUZGtkqiwdG7x+MhsS6RwQMGq0VyDoeDw4cPo0/Sk5SVhPeQl/yCfBSzgiZagyZMgznOTHxKvJrENBoNYWFhhIWFtXgdn89HQ0MDfr+fiIgINTHuXLyTg5sPkjoslWnXTGvRuCdY2Hd0zIB6pO+RHA4HeqOejJwMFEUha2AWTfVNlK0roze9uf7q60lP/6GBktVqxev1ttu3P7gFMlgYeeRWvpUrV/LBBx+Qk5ODoijceOONDBs2jJkzZ7Jy5UrmzZtHRESEOkMUrBMJXshoNBo++ugjzGYzF110Ube6AJCRvxCiU+osRX1BgUAAq9WK0WhscRxvkEajUbehabVafD4fNTU1JCQkdGj9PdjBLi4ujvDw8DZHvMGpeqfTSVNTE4VFhViaLNh8Npr8Tbg0zb0J9DF6zHFmtZ4geKRwcJkiGI/H5WHVW6uoOFxBzuQchk0Zpsaj0+lwuZrX6zsSPzR3+DMYDC0uOupK6qjeUM2E1AlMOW8KOp1O3RFgsViIiIhQR/HH+3yO3srndDoZN24ctbW1TJkyhejoaP7yl7+wcOFC7rnnHoqLi4mPj1efIzhTMWPGDJYsWcIHH3zA7bffzsaNGxk9enSH3uO5QpK/EKLT6WzT/MH1e5Op/a5/gUAAh8OB2+3Gbrdjs9lITEwkPDyciIiIYya34ME5x+pgF+T3+2lsbKSsrIzExET0ej1Op1OdJbDZbFTWVlJmKcPmae5N4Na7cRlcxKfFY45vvijwur2senMVDp+DsVeNJXfID0flKopCY2MjBoOhxTbEI9v0Hhlnex3+yvaW4djpYFb/WUyfNr3F94IV/QaDQZ31OPL5gp+bXq9XL4RiYmKwWq0tCghffPFFPvvsM6ZNm8aKFStISEjgoYce4oEHHmD69Ok8+uijrT7Diy66CI/Hw/fff8/y5csZNmwYgUAgpDUkZ5skfyFEp3IyB/KcSXa7nUAg0GoKvT0WiwWNRqMuCxw5pR8ULGKLiIjAarXi9/tJSEjocDxOp7NVx7vgLEHwdRRFoampidraWiwWCwAVlgoqGytxBBxs3rCZQHSAjIEZZPbNVLchGkwGtQNfWxc6R24RhOZ/r6amJuLj4wkLC0Oj0RAIBCjcVEh4STiXjLmE0aNHq891ZI/+9ir6A4GA+rm5XC7MZjNJSUnYbDZmzZqFoihs3LgRgEWLFnHnnXeyaNEiiouLefrpp2lqasLtdjN06FBef/31Vp9fnz590Gg0rF+/nqysrG7ZCEiSvxCiU+iM0/wVFRVqo5zjjd4DgQA1NTVERUUdd396cJagrKwMo9Go7vcPVq+31cEOmhvf6PV6YmJiOvQeLBYLTU1NREREqEV5waR6+PBhFEXB4XJQUltCg6uBBlcDTUoTESkRrXoTtHW6oc/nw+l0EhkZicfjab4wcHk4tP4QSfVJXDblMgYPHqy+n4706D+Sx+NBq9Wqn4/T6eSZZ57h+eefp1+/fqxYsQKAGTNmkJ6ezn/+8x++/PJL3n33XT777DOcTicrV65kypQpwA8nGi5evJjRo0er3QS7W+IHKfgTQnQCnWnvPvwwzZ+QkIBGo1ETZmNjo3qfI0fvwUY2ycnJHUokwTa9OTk5LUa/wdex2Wwt7m80GrHb7SQkJLR7YXC06upqzGZzizXvI18nNTW1xXa30tJSPB4PBoOBxsZGKusqKdtbhs1nozJQiT/cjyZao/Ym0IXrMJgNahV9WFgYilehfEM5gxjElfOuJCkpCZfLhc1mw+l0YrVaSU5Oxm63q1P67TlyKx80J26TycS9995LRkYGv/71r5k+fTqLFi1i3rx5/Pvf/8Zut3PJJZdgMpmw2Wzk5eW12DYY/D914YUXAs0XL931FEAZ+QshQuZUD+Q5Ezo6zR9ch66qqsLpdKrT9u2N3svKykhISFATf1JSUofeq8vloqKigqioKHWqHdrvc9+RafWjVVZWquvoRxYYBrv/BQsM6xvqKa0rpbiqGKfiRAlTCEQG0EXrCDOHYT9kZ2TMSOZcOIfY2Fj1+YMV/cHP6MgeCEFHFky63e42Z1qCI3eXy8XixYu5/fbbmThxIn/84x+ZMmUKTz/9NDfddBOKorBt2zbKy8u59NJLO/QZdDeS/IUQIdHZivqOrObv6DRwcHR9ZJvettb46+vrue+++3A4HHz66afExcXh9/spLi4mJiamzdE5tL++Dz+stR/ZWdDlcuF0OsnOzu5QhX5wR8KxLhSCh+w4nU4AqqqqCA8PV48sttlsVNdVU1pXSnZyNrNnzW5xQWKxWNDpdMddqgguhTQ0NJCVlXXcCxefz8e3337LvHnzGDVqlNrp77XXXmvVdKm7FfN1RPec7xBChNSRB/KEulNfUFNTE/DDOvOxegoEk2Zb0/zBHvxHCibPnj174vV6qa6u5sCBA9x22214vV7ee+89datZQ0MDVqtVPemvvaNsdTpdiyRntVoBSE5OpqmpicbGRnWkrNPp1NmI4Gfd0R0GOp2OyMhIIiIiqKqqol+/fhgMhhYXOf3oB6BucQwm2+rqavWxHaHVaunVq1eH/j/o9XqmT5/Ol19+ybx58ygsLCQ1NbXFRdeRzytakuQvhDhrOltR35GO7AAX3A/u8XjUjnLBeoRgd7+0tLTjPmew/W5xcTF1dXVcc801JCcnY7Va+eKLL2hoaGD06NHYbDZqampwu938v//3/1ixYgUffPABo0aN6lDswRPwghcKRy9ZBEfvdXV1ANhsNtxuN+np6fh8vuPOErRVqNfWRU5wKaSuro6KigoSExPVsw/aO4o3GJ/H4yE2NvaE/z+MHj2aJUuWMGXKFCoqKigvLycxMfGEnqM7kuQvhDgrgomwsxT1HUtbneuC28/cbjfR0dG4XC4URUGn07VbqxBMspGRkdhsNvr1ax4hv/HGG+Tn5zNlyhRSU1NJS0sjKSmJN954g/Xr1/Pb3/6W7OxsqqurW8R0dAIN7jCIiYk5ZiFgcPQeGRlJfX09CQkJxMTE4Ha7cTqdLQoZj25WFFx66MjFjlarVdsHDx48uEVnvaMLGYN7+YPbA4+sETgRiqLQu3dvtm7dSllZGUOHDj2p5+luJPkLIc6oznYgz8kKVve31TI32Pv+yIK8hoYGIiIiSEpKYu/evXg8HnJzc6muruall17iz3/+M9u3b8disZCWlkZtbS3PPfccl1xyCVdffTWxsbHq9jytVquuiQcTaHA0npWV1aGK9UAgQHV1dYujctt6P8HXqa+vV3sWBA/b6UizosbGxlZLCTqdjqioqBazK4FAALvd3tzS+BRG6hqNBr/fT0pKCikpKbK+30GS/IUQZ8yRRX2dbZr/dGlvliDYBtjtdnP48GFMJhOBQIAnnniC3NxcrrrqKjZt2oRer8fn8/HMM88AcP/996uj4CPrCY5MoMEdCYMHD8btdmOz2Voc4nP0LMGxahSOptVqiYyMxOFwkJ6erhYzHm+7o91uP2aP/qMF++t39HCkYznyPUni7xhJ/kKIM6KzHchzNgUPowkqKysjPj6eZcuWsXDhQt566y0aGxuprq4mJiaGoqIiPvnkEx544AGSk5NxOp289957bNiwgaysLG644Qays7OBHzoIBpNs8NCbIx05zX5kYV+w4c+xZgqCWwWPPpPgWGv8hw4dIhAIEBMTQ3V1dbvbEIOcTudxZxHEmSXJXwhxWh1Z1KfRaDAajefcaL+jgtX2FRUVFBYW8vrrr3P99ddz/vnns2fPHnXU/tJLL5Gdnc2Pf/xjXC4XNTU1REREEBUVxcKFC8nNzSU7O5uKigpiYmKOWz0fnCVQFAWtVkuPHj3URG2z2dSLMmg5S3AiMwTQfJFjs9lITU1ttd0xuA3wyM8iPDxc3aXQXZvrdBby6QshTpvOtnc/1IKfw7Zt27Db7QwZMoRf/OIXQPPWPIfDwerVqxk1ahSPPPII0dHR+P1+oqOjyc7OJjY2lsbGRhISEigrKyMqKqrDo+XgDoBgY50jj8Y9UrBfQHV1tbpeX1dX1+JgnfbeW1szBNA8S2AwGFqs8QcPJIqPj+9Ws0CdVYeTf01NzZmMQ4gur7392N3FkQfydNWivtMtmORSUlIwmUz89re/JScnB2jucrdp0ybq6+u59dZbmTFjhvqYQCCAwWCgqqoKrVZLbm4uOTk5+P3+VlsQg4/R6XRqYWBHdgAcHaPZbCYrKwvguLMEer3+hGYIglv5UlNTu/XFYGfS4eSfnJx8JuMQosvr7s0yu8IWvlBZuHBhq9tMJhNms5mxY8dy+eWXt/jMghdOwQ6AwfX9YJI/MqkHZ1s8Hg9er5fGxkYiIiLQaDQd6l1/9AxB8PXbmyWoq6ujurqapKQkLBZLq+N3j+bz+fD7/Se9lU+cGTLtL4Q4LYIjQEn8rbWVhMeOHUtxcTFer7fNVrY+n4/q6mp69OhxzMQZnGkJPkew619wtN3WLIFer0dRFKqrq4mNje3wYUFOpxONRsPgwYPV24L9D9qaJTAajYSFhbVqtytCT5K/EOK0kKTfvrZGxIFAQE3cbSktLcVms530rKtOp2s1cj9ylsButxMZGYmiKLjd7uPuyGhoaECj0bRa3mqv/4HdbsdgMBAZGXlS8YszS5K/EEKEQHs1EU6nE5PJhMPhwGw2M2zYMOCHnQOn4shZgiOr8483S1BTU9PqAKNjcTqdREZGHvdkRBE6HU7+R7aZFEIIcWZ89913/PKXv6SgoECtlk9LS6NHjx5nbHalvVkCj8eD2+1Wt+g5nc5jHnqkKAoulwuz2dzh44RFaMiRvkII0clYrVa2bdvG5s2b+fTTT5k5cyYPPvhgi61zoRKcJQiu7wf/6HQ6fD4fMTExstOjC5DkL4QQ4pQEZwm6c0OnrkaSvxBCdEKBQKDFUcJCnE6S/IUQQohuRhZmhBBCiG5Gkr8QQgjRzUjyF0IIIboZSf5CCCFENyPJXwghhOhmJPkLIYQQ3YwkfyGEEKKbkeTfBfzqV79Sz/MOeuihh9BoNPzrX/9Sb6usrMRgMPDqq6+e7RCFEEJ0IZL8u4DY2Fjsdrv6tdPp5I033kCv19PQ0KDe/uabb2I2m7nhhhtCEKUQQoiuQpJ/FxAbG4vT6SQQCADw7rvvotfrmTlzppr8A4EAr732Gj/72c86fOymEEKI7kmSfxcQGxuLoig0NTUB8MILL3DrrbeSmJioJv+lS5dSVFTEHXfcEcJIhRBCdAWS/LuA2NhYAOx2O2vWrGHnzp3cfvvtREdHq8n/lVdeYcaMGfTv3z90gQohhOgSJPl3AUcm/xdeeIE5c+bQo0cPNfmXl5eTl5fHnXfeGdpAhRBCdAlyTmQXEEz++fn5fPrppyxevBhATf5vvPEGKSkpzJkzJ4RRCiGE6Cpk5N8FBJP/U089RW5uLjNmzACak7/FYuH111/n9ttvlzO/hRBCdIhkiy4gmPxXrFjB888/r94eHR1NYWEhBoOBW2+9NUTRCSGE6Gok+XcB0dHRaDQazGYzP/3pT9XbY2JiALjyyitJTU0NVXhCCCG6GI2iKEqogxBCCCHE2SNr/kIIIUQ3I8lfCCGE6GYk+QshhBDdjCR/IYQQopuR5C+EEEJ0M5L8hRBCiG5Gkr8QQgjRzUjyF0IIIboZSf5CCCFENyPJXwghhOhmJPkLIYQQ3YwkfyGEEKKbkeQvhBBCdDOS/IUQQohuRpK/EEII0c1I8hdCCCG6GUn+QgghRDcjyV8IIYToZiT5CyGEEN2MJH8hhBCim5HkL4QQQnQzkvyFEEKIbkaSvxBCCNHNSPIXQgghuhlJ/kIIIUQ3I8lfCCGE6GYk+QshhBDdjCR/IYQQopuR5C+EEEJ0M/qO3ElRFGw225mORYguLyoqCo1GE+owhBDimDqU/G02GzExMWc6FiG6vMbGRqKjo0MdhhBCHJNGURTleHfqLCN/q9VKjx49KCkp6fa/YOWz+EFn+ixk5C+E6Ao6NPLXaDQh/6V6pOjo6E4VTyjJZ/ED+SyEEKJjpOBPCCGE6GYk+QshhBDdTJdK/mFhYfzhD38gLCws1KGEnHwWP5DPQgghTkyHCv6EEEIIce7oUiN/IYQQQpw6Sf5CCCFENyPJXwghhOhmJPkLIYQQ3UyXTP5FRUXcfPPN9OrVC5PJRO/evfnDH/6Ax+MJdWhnxb/+9S+ys7MJDw9n3LhxbNy4MdQhnXVPPPEEY8aMISoqiuTkZK644gr2798f6rCEEKJL6JLJf9++fQQCAV555RV2797N008/zcsvv8z//d//hTq0M+6DDz7g/vvv5w9/+ANbt25l2LBhXHDBBVRXV4c6tLNq1apV3Hnnnaxfv55ly5bh9XqZPXs2TU1NoQ5NCCE6vXNmq9/f//53XnrpJQoLC0Mdyhk1btw4xowZwwsvvABAIBCgR48e3H333Tz88MMhji50ampqSE5OZtWqVUyZMiXU4QghRKfWJUf+bWlsbCQ+Pj7UYZxRHo+HLVu2MGvWLPU2rVbLrFmzWLduXQgjC73GxkaAc/7/gBBCnA7nRPIvKCjg+eef5/bbbw91KGdUbW0tfr+flJSUFrenpKRQWVkZoqhCLxAI8Ktf/YpJkyYxePDgUIcjhBCdXqdK/g8//DAajeaYf/bt29fiMWVlZVx44YXMnTuXW2+9NUSRi1C688472bVrF++//36oQxFCiC6hQ0f6ni2//vWvufHGG495n5ycHPXv5eXlTJ8+nYkTJ/Lqq6+e4ehCLzExEZ1OR1VVVYvbq6qqSE1NDVFUoXXXXXeRl5fH6tWryczMDHU4QgjRJXSq5J+UlERSUlKH7ltWVsb06dMZNWoUb731Flptp5rEOCOMRiOjRo1i+fLlXHHFFUDzlPfy5cu56667QhvcWaYoCnfffTf//e9/WblyJb169Qp1SEII0WV0quTfUWVlZUybNo2ePXvy1FNPUVNTo37vXB8B33///fzsZz9j9OjRjB07lmeeeYampiZ+/vOfhzq0s+rOO+/k3Xff5fPPPycqKkqteYiJicFkMoU4OiGE6Ny65Fa/f//73+0muy74dk7YCy+8wN///ncqKysZPnw4zz33HOPGjQt1WGeVRqNp8/a33nrruEtHQgjR3XXJ5C+EEEKIk3fuL5QLIYQQogVJ/kIIIUQ3I8lfCCGE6GYk+QshhBDdjCR/IYQQopuR5C+EEEJ0M5L8hRBCiG5Gkr8QQgjRzUjyF0IIIboZSf5CCCFENyPJXwghhOhmJPkLIYQQ3cz/BzUGkPRaJwqfAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 600x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot a single input quadratic in both two and three dimensions\n",
    "func1 = lambda w: w**2  + 3\n",
    "func2 = lambda w: w[0]**2 + w[1]**2  + 3\n",
    "\n",
    "# use custom plotter to show both functions\n",
    "section_3_2_helpers.compare_2d3d(func1 = func1,func2 = func2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kNEItKpvOXC0"
   },
   "source": [
    "This sort of first order behavior is universal regardless of the function one examines and - moreover - it holds regardless of the dimension of a function's input: first order derivatives are always zero at the minima of a function.  This is because minimum values of a function are naturally located at 'valley floors' where a tangent line or hyperplane tangent to the function is perfectly flat, and thus has zero-valued slope(s)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D3-MOLbmOXC1"
   },
   "source": [
    "Because the derivative/gradient at a point gives precisely this slope information, the value of first order derivatives provide a convenient way of *characterizing* minimum values of a function $g$. When $N=1$ any point $v$ where \n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\mathrm{d}}{\\mathrm{d}w}g\\left(v\\right)=0\n",
    "\\end{equation}\n",
    "\n",
    "is a potential minimum. Analogously with general $N$ dimensional input, any $N$ dimensional point $\\mathbf{v}$ where *every* partial derivative of $g$ is zero, that is\n",
    "\n",
    "\\begin{equation}\n",
    "\\\n",
    "\\frac{\\partial}{\\partial w_{1}}g(\\mathbf{v})=0\\\\\n",
    "\\frac{\\partial}{\\partial w_{2}}g(\\mathbf{v})=0\\\\\n",
    "\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\vdots \\\\\n",
    "\\frac{\\partial}{\\partial w_{N}}g(\\mathbf{v})=0\n",
    "\\end{equation}\n",
    "\n",
    "is a potential minimum. This system of $N$ equations is naturally referred to as the *first order system of equations*.  We can write the first order system more compactly using gradient notation as \n",
    "\n",
    "\\begin{equation}\n",
    "\\nabla g\\left(\\mathbf{v}\\right)=\\mathbf{0}_{N\\times1}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XJJINT4pOXC1"
   },
   "source": [
    "This is a very useful characterization of minimum points because - at least in principle - it gives us a concrete alternative to seeking out a function's minimum points directly via some zero-order approach: by solving a function's first order system of equations.\n",
    "\n",
    "> The first order optimality condition translates the problem of identifying a function's minimum points into the task of solving a system of $N$ first order equations.\n",
    "\n",
    "There are however two problems with the first order characterization of minima.  First off, with few exceptions (including some important examples we detail in the next Subsection), it is virtually impossible to solve a general function's first order systems of equations 'by hand'.   That is, to solve such equations algebraically for 'closed form' solutions one can write out on paper.  This is where the local first and second order optimization methods we discuss in the current and subsequent Chapters come in - they are iterative ways of solving such a system.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "K5329m8OOXC1"
   },
   "source": [
    "The other problem is that the *first order optimality condition* does not only define minima of a function, but other points as well.  The first order condition also equally characterizes *maxima* and *saddle points* of a function -  as we see in a few simple examples below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "CfYOz052OXC2"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 1:</span> Finding points of zero derivative for single-input functions graphically"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OJ0-H8AvOXC2"
   },
   "source": [
    "In the next Python cell we plot the three functions\n",
    "\n",
    "\\begin{equation}\n",
    "\\\n",
    "g(w) = \\text{sin}\\left(2w\\right) \\\\\n",
    "g(w) = w^3 \\\\\n",
    "g(w) = \\text{sin}\\left(3w\\right) + 0.1w^2\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4ZxTl7mxOXC2"
   },
   "source": [
    "\n",
    "in the top row of the figure. For each we mark all the zero derivative points in green and draw the first order Taylor series approximations/tangent lines there in green as well. Below each function we plot its first derivative, highlighting the points where it takes on the value zero as well (the horizontal axis in each case is drawn as a horizontal dashed black line). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 369
    },
    "id": "Urw9557jOXC2",
    "outputId": "69ce8c53-31e5-4123-d4cf-d6ac4c1875b1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot a single input quadratic in both two and three dimensions\n",
    "func1 = lambda w: np.sin(2*w)\n",
    "func2 = lambda w: w**3\n",
    "func3 = lambda w: np.sin(3*w) + 0.1*w**2\n",
    "\n",
    "# use custom plotter to show both functions\n",
    "section_3_2_helpers.show_stationary(func1 = func1,func2 = func2,func3 = func3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "KIFGHNOAOXC3"
   },
   "source": [
    "Examining these plots we can see that it is not only *global* minima that have zero derivatives, but a variety of other points as well. These consist of \n",
    "\n",
    "- *local minima* or points that are the smallest with respect to their immediate neighbors, like the one around the input value $w=2$ in the right panel\n",
    "\n",
    "\n",
    "- *local and global maxima* or points that are the largest with respect to their immediate neighbors, like the one around the input value $w=-2$ in the right panel\n",
    "\n",
    "\n",
    "- *saddle points* like the one shown in the middle panel, that are neither maximal nor minimal with respect to their immediate neighbors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3oMuBaltOXC3"
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "1aSMCWfVOXC3"
   },
   "source": [
    "The previous example illustrate the full swath of points having zero-valued derivative(s) - and this includes multi-input functions as well *regardless of dimension*.  Taken together all such points are collectively referred to as *stationary points* or *critical points*.\n",
    "\n",
    "> Together local/global minima and maxima, as well as saddle points are referred to as *stationary points*.  These are points at which a function's derivative(s) take on zero value, i.e., $\\nabla g(\\mathbf{w}) = \\mathbf{0}_{N\\times 1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rbGlQiokOXC3"
   },
   "source": [
    "So - while imperfect in terms of the points it characterizes - this *first order condition for optimality* does characterize points of a function that include a function's global minima.  Moreover the first order condition allows us to translate the problem of finding global minima to the problem of solving a system of (typically nonlinear) equations, for which many algorithmic schemes have been designed.\n",
    "\n",
    "> **The first order condition for optimality**: Stationary points of a function $g$ (including minima, maxima, and\n",
    "saddle points) satisfy the first order condition $\\nabla g\\left(\\mathbf{v}\\right)=\\mathbf{0}_{N\\times1}$.  This allows us to translate the problem of finding global minima to the problem of solving a system of (typically nonlinear) equations, for which many algorithmic schemes have been designed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hss_k4joOXC3"
   },
   "source": [
    "Note: if a function is *convex* - as with the quadratic function's shown in the beginning of this Subsection - then any point of such a function satisfying the first order condition must be a global minima, as a convex function has no maxima or saddle points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "code_folding": [],
    "id": "mza-i9KmOXC3"
   },
   "source": [
    "##  Special cases where the first order system can be solved 'by hand'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2e1nAVb7OXC3"
   },
   "source": [
    "In principle the benefit of using the first order condition is that it allows us to transform the task of seeking out global minima to that of solving a system of equations, for which a wide range of algorithmic methods have been designed. The emphasis here on *algorithmic* schemes is key, as solving a system of equations *by hand* is generally speaking very difficult (if not impossible).  Again we emphasize, the vast majority of (nonlinear) systems of equations cannot reasonably be solved by hand.\n",
    "\n",
    "However there are a handful of relatively simple but important examples where one can compute the solution to a first order system by hand, or at least one can show algebraically that they reduce to a *linear system of equations* which can be easily solved numerically.  By far the most important of these are the multi-input quadratic function and the highly related *Rayleigh quotient*, which we discuss below.  We will see the former later on when discussing linear regression, and the latter in a number of instances where we use it as a tool for studying the properties of certain machine learning cost functions.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tbI2LzuTOXC4"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 2:</span> Calculating stationary points of some single-input functions algebraically"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LLRwyABKOXC4"
   },
   "source": [
    "In this Example we use the first order condition for optimality to compute stationary points of the functions \n",
    "\n",
    "\\begin{equation}\n",
    "g\\left(w\\right)=w^{3} \\\\\n",
    "g\\left(w\\right)=e^{w} \\\\\n",
    "g\\left(w\\right)=\\textrm{sin}\\left(w\\right)\\\\\n",
    "g\\left(w\\right)=a + bw + cw^{2}, \\,\\,\\,c>0 \\\\\n",
    "\\end{equation}\n",
    "\n",
    "and will distinguish the kind of stationary point visually for these instances."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qs3l3dXWOXC4"
   },
   "source": [
    "- $g\\left(w\\right)=w^{3}$, plotted in the middle panel of the second figure above, the first order condition gives $g'\\left(v\\right)=3v^{2}=0$ which we can visually identify as a saddle point at $v=0$.\n",
    "\n",
    "\n",
    "- $g\\left(w\\right)=e^{w}$, the first order condition gives $g'\\left(v\\right)=e^{v}=0$ which is only satisfied as $v$ goes to $-\\infty$, giving a minimum.\n",
    "\n",
    "\n",
    "- $g\\left(w\\right)=\\text{sin}\\left(w\\right)$ the first order condition gives stationary points wherever $g'\\left(v\\right)=\\text{cos}\\left(v\\right)=0$\n",
    "which occurs at odd integer multiples of $\\frac{\\pi}{2}$, i.e., maxima at $v=\\frac{\\left(4k+1\\right)\\pi}{2}$ and minima at $v=\\frac{\\left(4k+3\\right)\\pi}{2}$\n",
    "where $k$ is any integer. \n",
    "\n",
    "\n",
    "- $g\\left(w\\right)=w^{2}$ for which the first order condition gives $g'\\left(v\\right)=2cv + b =0$ with a minimum\n",
    "at $v=\\frac{-b}{2c}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FyBqLbllOXC4"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 3:</span> A simple looking function with difficult to compute (algebraically) global minimum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "tYSwKLl6OXC4"
   },
   "source": [
    "As mentioned previously the vast majority of functions - or to be more precise the system of equations derived from functions - cannot be solved by hand algebraically.  To get a sense of this challenge here we show an example of a simple-enough looking function whose global minimum is very cumbersome to compute by hand.  \n",
    "\n",
    "Take the simple degree four polynomial\n",
    "\n",
    "\\begin{equation}\n",
    "g(w) = \\frac{1}{50}\\left(w^4 + w^2 + 10w\\right)\n",
    "\\end{equation}\n",
    "\n",
    "which is plotted over a short range of inputs containing its global minimum in the next Python cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 225
    },
    "id": "6h8jkLyNOXC4",
    "outputId": "40481e89-366c-4df8-fa06-ceeb9d08054e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 600x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# specify range of input for our function\n",
    "w = np.linspace(-5,5,50)\n",
    "g = lambda w: 1/50*(w**4 + w**2 + 10*w)\n",
    "\n",
    "# plot\n",
    "figure = plt.figure(figsize=(6,3))\n",
    "plt.plot(w,g(w),linewidth=2,color='k')\n",
    "plt.xlabel('$w$',fontsize=14)\n",
    "plt.ylabel('$g(w)$',rotation=0,labelpad=15,fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "j3UEuum4OXC4"
   },
   "source": [
    "The first order system here can be easily computed as \n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\mathrm{d}}{\\mathrm{d} w}g(w) = \\frac{1}{50}\\left(4w^3 + 2w + 10\\right) = 0\n",
    "\\end{equation}\n",
    "\n",
    "which simplifies to\n",
    "\n",
    "\\begin{equation}\n",
    "2w^3 + w + 5 = 0\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6dPoRzjYOXC5"
   },
   "source": [
    "This has three possible solutions, but the one providing the minimum of the function $g(w)$ is \n",
    "\n",
    "\\begin{equation}\n",
    "w = \\frac{\\sqrt[\\leftroot{-2}\\uproot{2}3]{\\sqrt[\\leftroot{-2}\\uproot{2}]{2031} - 45}}{6^{\\frac{2}{3}}} - \\frac{1}{\\sqrt[\\leftroot{-2}\\uproot{2}3]{6\\left(\\sqrt{2031}-45\\right)}}\n",
    "\\end{equation}\n",
    "\n",
    "which can be computed - after much toil - using [centuries old tricks developed for just such problems](http://mathworld.wolfram.com/CubicFormula.html). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "66EgJlCwOXC5"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 4:</span> Stationary points of a general multi-input  quadratic function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ZnXLwQ-TOXC5"
   },
   "source": [
    "Take the general multi-input quadratic function\n",
    "\n",
    "\\begin{equation}\n",
    "g\\left(\\mathbf{w}\\right)=a + \\mathbf{b}^{T}\\mathbf{w} + \\mathbf{w}^{T}\\mathbf{C}\\mathbf{w}\n",
    "\\end{equation}\n",
    "\n",
    "where $\\mathbf{C}$ is an $N\\times N$ symmetric matrix, $\\mathbf{b}$ is an $N\\times 1$ vector, and $a$ is a scalar.\n",
    "\n",
    "Computing the first derivative (gradient) we have\n",
    "\n",
    "\\begin{equation}\n",
    "\\nabla g\\left(\\mathbf{w}\\right)=2\\mathbf{C}\\mathbf{w}+\\mathbf{b}\n",
    "\\end{equation}\n",
    "\n",
    "Setting this equal to zero gives a *symmetric and linear* system of equations of the form\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{C}\\mathbf{w}=-\\frac{1}{2}\\mathbf{b}\n",
    "\\end{equation}\n",
    "\n",
    "whose solutions are stationary points of the original function.  Note here we have not explicitly solved for these stationary points, but have merely shown that the first order system of equations in this particular case is in fact one of the easiest to solve numerically."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RgS83uAUOXC5"
   },
   "source": [
    "##  Coordinate descent and the first order optimality condition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UKHMdB1AOXC5"
   },
   "source": [
    "As we have seen thus far the first order optimality condition is a powerful way of characterizing the stationary points - and in particular the minima - of a function.  In particular it tells us that - for a given cost function $g\\left(\\mathbf{w}\\right)$ taking in $N$ dimensional input - that the stationary points (minima included) of this function are those satisfying the system of equations\n",
    "\n",
    "\\begin{equation}\n",
    "\\nabla g\\left(\\mathbf{v}\\right)=\\mathbf{0}_{N\\times1}\n",
    "\\end{equation}\n",
    "\n",
    "or written out one equation at-a-time as\n",
    "\n",
    "\\begin{equation}\n",
    "\\\n",
    "\\frac{\\partial}{\\partial w_{1}}g(\\mathbf{v})=0\\\\\n",
    "\\frac{\\partial}{\\partial w_{2}}g(\\mathbf{v})=0\\\\\n",
    "\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\vdots \\\\\n",
    "\\frac{\\partial}{\\partial w_{N}}g(\\mathbf{v})=0.\n",
    "\\end{equation}\n",
    "\n",
    "If this set of equations can be solved (as it can be for the examples above) we can then potentially recover minimum points of $g$.   However we can rarely solve this system directly in practice 'by hand', and even when we can - e.g., when the set of equations is linear - we still need an algorithm to actually resolve the solution to such a system in a timely manner. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uGBoNVW2OXC5"
   },
   "source": [
    "However if we take a 'coordinate-wise' view of things, we can simplify the task of solving first order systems by solving just one of these equations (or - more generally - one batch of the equations) at a time resulting in a coordinate descent scheme.  This turns the often impossible task of solving a first order systems *simultaneously* into a coordinate-wise approach where we solve them *sequentially*.  That is, instead of trying to solve the system of equations all at once we solve each partial derivative equation\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial}{\\partial w_{n}}g(\\mathbf{v})=0\n",
    "\\end{equation}\n",
    "\n",
    "one at-a-time.  Hence this idea will be especially effective when each such equation of a first order system can be solved for in closed form.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "eeaYdgMcOXC5"
   },
   "source": [
    "To perform coordinate descent using this idea we first initialize at an input point $\\mathbf{w}^0$, and begin by updating the first coordinate\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial}{\\partial w_{1}}g\\left(\\mathbf{w}^0\\right)=0 \n",
    "\\end{equation}\n",
    "\n",
    "for the optimal first weight $w_1^{\\star}$.  We then update the first coordinate of the vector $\\mathbf{w}^0$ with this solution, and call the updated set of weights $\\mathbf{w}^1$.  Continuing this pattern to update the $n^{th}$ weight we solve\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial}{\\partial w_{n}}g\\left(\\mathbf{w}^{n-1}\\right)=0 \n",
    "\\end{equation}\n",
    "\n",
    "for $w_n^{\\star}$, and update the $n^{th}$ weight using this value forming the updated set of weights $\\mathbf{w}^n$.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_9Je8gp9OXC6"
   },
   "source": [
    "After we sweep through all $N$ weights a single time we can refine our solution by sweeping through the weights again (as with any other coordinate wise method).  At the $k^{th}$ such sweep we update the $n^{th}$ weight by solving the single equation\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial}{\\partial w_{n}}g\\left(\\mathbf{w}^{k + n-1}\\right)=0 \n",
    "\\end{equation}\n",
    "\n",
    "and update the $n^{th}$ weight of $\\mathbf{w}^{k + n-1}$, and so on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "V9kJ6VgZOXC6"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 5:</span>  Minimizing convex quadratic functions via first order coordinate descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "id": "1dszZMFKOXC6"
   },
   "outputs": [],
   "source": [
    "def coordinate_descent_for_quadratic(g,w,max_its,a,b,C):\n",
    "    '''\n",
    "    Coordinate descent wrapper for general quadratic function. Here\n",
    "    \n",
    "    a - a constant\n",
    "    b - an Nx1 vector\n",
    "    C - an NxN matrix (symmetric and all nonnegative eigenvalues)\n",
    "    '''\n",
    "        \n",
    "    # record weights and cost history \n",
    "    weight_history = [copy.deepcopy(w)]     \n",
    "    cost_history = [g(w)]\n",
    "    N = np.size(w)\n",
    "    \n",
    "    # outer loop - each is a sweep through every variable once\n",
    "    for k in range(max_its):\n",
    "        # inner loop - each is a single variable update\n",
    "        for n in range(N):\n",
    "            w[n] = -(np.dot(C[n,:],w) - C[n,n]*w[n] + 0.5*b[n])/float(C[n,n])\n",
    "            \n",
    "            # record weights and cost value at each step\n",
    "            weight_history.append(copy.deepcopy(w))\n",
    "            cost_history.append(g(w))\n",
    "\n",
    "    return weight_history,cost_history"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TcK4bOBQOXC6"
   },
   "source": [
    "First we use this algorithm to minimize the simple quadratic \n",
    "\n",
    "\\begin{equation}\n",
    "g(w_0,w_1) = w_0^2 + w_1^2 + 2\n",
    "\\end{equation}\n",
    "\n",
    "which can be written in vector-matrix where $a = 2$, $\\mathbf{b} = \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}$, and $\\mathbf{C} = \\begin{bmatrix} 1 \\,\\, 0 \\\\ 0 \\,\\, 1 \\end{bmatrix}$.  We initialize at $\\mathbf{w} = \\begin{bmatrix} 3 \\\\ 4 \\end{bmatrix}$ and run $1$ iteration of the algorithm - that is all it takes to perfectly minimize the function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 333
    },
    "id": "4twaCzIUOXC6",
    "outputId": "137f7dff-a8de-490c-cb2c-30c1e1a5ee1b",
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/k9/0vtmhf0s5h56gt15mkf07b1r0000gn/T/ipykernel_54511/2670033010.py:19: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  w[n] = -(np.dot(C[n,:],w) - C[n,n]*w[n] + 0.5*b[n])/float(C[n,n])\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x450 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define constants for a N=2 input quadratic\n",
    "a = 2\n",
    "b = np.zeros((2,1))\n",
    "C = np.eye(2)\n",
    "\n",
    "# a quadratic function defined using the constants above\n",
    "g = lambda w: (a + np.dot(b.T,w) + np.dot(np.dot(w.T,C),w))[0]\n",
    "\n",
    "# initialization\n",
    "w = np.array([3,4])\n",
    "\n",
    "# run your alternating descent code\n",
    "max_its = 1\n",
    "weight_history,cost_history = coordinate_descent_for_quadratic(g,w,max_its,a,b,C)\n",
    "\n",
    "# show run in both three-dimensions and just the input space via the contour plot\n",
    "plotter.two_input_contour_plot(g,weight_history,xmin = -1.5,xmax = 4.5,ymin = -1.5,ymax = 4.5,num_contours = 30,show_original = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QddJL7tjOXC7"
   },
   "source": [
    "Next we make a run of $2$ iterations of the method at the same initial point to completely minimize another convex quadratic with $a = 20$, $\\mathbf{b} = \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}$, and $\\mathbf{C} = \\begin{bmatrix} 2 \\,\\, 1 \\\\ 1 \\,\\, 2 \\end{bmatrix}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 333
    },
    "id": "SK0U6ASkOXC7",
    "outputId": "31540d68-0b62-4a91-9541-0b9d2297d908"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/k9/0vtmhf0s5h56gt15mkf07b1r0000gn/T/ipykernel_54511/2670033010.py:19: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  w[n] = -(np.dot(C[n,:],w) - C[n,n]*w[n] + 0.5*b[n])/float(C[n,n])\n"
     ]
    },
    {
     "data": {
      "image/png": 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+JX79ho0XiV8yuR8/RHhYKDVq/DrxA6hZE6pXh6tXQ2lWo7h6AszAIr985uSGhZzcsFDTofx1ZLGRvHOdkryLF5F04se/ty8Cyim/DL57LN0kf5ZlGwIK/I4tIfHVOZBI0SnZ7ocEUNu2EsgTib+zBZnvdRSk+7/lC4KQDojkTxCEVHF2dqZx48Y4Ojr+NvmLi4sjLi7u29fh4eHJmuOt1132zB0FQNuufek9eEzqA/7L3L15FVCe8UuO7t3h6lVo0waWLk3DwAQhjcTEQMGC/35REij7mweUBUoAXhAb+Bp5QixSnfSx6m1ZthHI5fidWEbiyzPKBLBEmx8TwNxVQZZI/H0X5L43NBStIAgZiUj+BEFIMVdXV+7fv8+dO3eSdf3cuXOZPn16iuYICfBj68SBJMbHU7NeY0ZMnieqeqZAdFQkoCzukhxfr5PJwMYmjYIShDQUFPSfL3In80G5AS/lf8riYtJN8gdgWb4JCoUM/5MrSfQ+BVItdIu3+uE67bw1UcgTSPDcrYEoBUHIaETyJwhCivj6+jJ06FDOnTuHfjLPho0fP54RI0Z8+zo8PBxbW9ufXh8fG8PWSQOICguhcLFSzFiyAS0trZ9eL/zI0EhZlTIwMHnXf71OSwv8fl1TQxDSpZj/1mx5n8wH/ec6LT3N9/z7X1krNEchl/Ph9GoSnx9HItVGp2izH67Tye+IxNiK+Gti2V4QhF8TyZ8gCCly7949Pn78SNmy/7+nSiaTceXKFVatWkVcXNwPiZqenh56enrJGl+hUHBg8SQ+vHqGcRZLFq7bhYFotJ1i5StX5+RhV1xclJU9f8fFRfnZvugCngb8uLog/FrgBz9c1i3hwumjAOjo6uHQojPVWnVDz8BQw9FlTk9vXGDfoskoZAkYWBfEruU49LPNIPbTO2U7h/v8euvnPb6t+unnyJeuVv3+K1ullihkiQScW0/CUzfQ0kGnUMMfrtOyzK/+4ARByHBEtU9BEFIkIiKC9++//7N6z549KVy4MGPHjqV48d8XDPlVtc+bx/eyf+EEpFparNlxhLKVqqk0/r/Ff6t9XrqkLOryM9+qfZqZc+TSQ4xNf99LTUja00cPWD53Ig9uK89fmWa1onHfUZSt3+Kv76GYFt48usu60X2QxUagZ2lDllL1CLywVXlnBq32+TNBV3cTeEHZ+F6nVEd0CtT77n5FQgwxR5zFeyVByCREtU9BENIFExOTHxI8IyMjLC0tk5X4/Urgu5ffKnsOHDlZJH6/oVAo+PwpCN/3b/jg+55Af18+Bn4g+FMgIcGfvtX+a9kSDh9OOgG8fFl5P0BEWCh1yuRGV1cPYxNTjE3NMDO3IIulJZZZrbDMbkV2q5xYWefCKqcNOW1zo6+f/rbKaVLRkmVYt/sEl84eY/ncyXzwfc+euaO5fmQXLYdMwa5IKU2HmKnkLVmekesPsHFMT74E+fHplhta+ibIYiOUiZ0Tyqqe/10BvA+M4lvip21ojnmJuuoOPcWsqndCkRhP0JWdJDzcg0RLF+28v/irjiAIQhJE8icIQrqQmBDPrpkjSIiLpVL1OnTtO0TTIaUr8XFxvHz+mGdeD/B+6sUr76e8ffmCqMjfV0798kW5sle9urKqZ44cyjN+Li7KCp8/zBUfR8jnT4R8/vTbsbNZWWOTOw+58xTAPn9B8uQvTL6CRchmZf3XFuiRSCTUdmpG1VpO7Nm6hk2rFuHz1JPlA1pRsVFbGvUbhUmWrJoOM9Owss/PP6v3s3FMLwLevECirYdEqo1CnqhM8MqhrOqZG+UZP6//f6xES4fc7aeipZsx/ohhVas78oQ4PnnsJ/7+dtDSRTu3g6bDEgQhAxHbPgVBULuktn2e2rQY9x1rMDTLwoEzN8mazUrDUWpWTHQUnnc8uHfrGg9u3+D5E08S4uN/uE4qlZLLxg7b3HnIaWOLdS4brKysscyWHcus2TA2McVt/25ct28mPDzsh8ebZ8lCr/5D6D9kFImJicRERxEdFUV4WCjh4WF8CQnmc/Angj995FNQIIEf/Png74e/nw+RET9PPE3Ns1CwSAkKFS1JkRJlKFqyLLns7P/KhDD4YyCrFkzj5GFXAPSNTWjYewRVmndGKgoZqUxMRDhbJw3gtectkGoh1dFDHhf90+u1Dc3J3X4qxnYl1Bjln1MoFPifXMnnu0dBIkW38kC0c5UT2z4FIZNJq/xHJH+CIKjd/yZ/ft6PWT6gFXKZjHmrXajToLmmQ9QIf593XHY/wbULZ/C860FiQsJ392exzEqJUmUoWrwURYqVpEChIuTOmz9ZxXT8/XypWa4Qbdoo2zloaUHRMotp17kH+gapW/UI/RLC+7eveffmNW9fe/PS+zmvvJ/z7vVLZDLZD9ebZbGgeOkKlCxbkVLlK1OsVDn09NJnkY208Oj+bRZOG8WLJ48AyFWgGK1HzCB30dKaDSwTSYiLY9es4XhdOQOAeYm6xH56R2zg62/X6OfIR9byTTEvUTfDrPj9L4VCju/RxXzxPAMSLfSqDkFqmV8kf4KQiYjkTyR/gpBp/Df509EzYPmAVvi/fIJjo5bMWblV0+GpVYC/D2ePHeTciUN4P/X67r5ctnY4VK1JxSrVKVvRgdz2eVO9cvY5+BOViuXG11fZx8/PDz6Ev8cyazZVPI3vxMXG8tL7GU+9HvL08UO8Htzj6ZNHP6xc6ujqUrx0eco71KC8Qw2KlyqPjq6uyuNJT2QyGYddt7FywXRiIsORSCRUbtqBRv1GY2giCu2oglwm4+DSKdw8plxpzVG7J1krt0IeH4uWnkG6reqZUgq5jPeH5hD25DJIddB1cCb++jLxXkkQMgmR/InkTxAyjf8mf7dPHuDIqlkYGJty6PxdLLNm13R4aS4uLpaLp49yZN8O7t38/0N3WlpaVHSoTp36jajl6IR93vwq2yapzuQvKfHx8Tx7/JD7d25x744H927d4NPHoO+uMTQyplzlajjUcMShpiO5bO3VEpsmhAR/YtWCqRw/qGzMbWxuQbPBkyjr2Oyv3BqragqFgtObl+C+Yw0AWSu3Jmf9/kgkmaviqlyWwPt90wn3vglaeiCLE++VBCGTEMmfSP4EIdP4+poet/M8S/s1Jy46kvGzltGyYw9Nh5amggL8ObBzE257XQj7EgIoi4NUqlKDJi3bUr9RMyws06YQiKaTv/+lUCh49+YVt65fwePaZTyuXf6hwEye/IWoVqcBNeo2pHiZCj/0j8wM7t++zvzJI3j76gUABStUp82IGVjmtNNwZJnDlf1bObJqFgBZStXHttlIJNLM9XskT4jjze4JRL17CCDeKwlCJiGSP5H8CUKm8fU1Xa5eC+6dc6NIiTJsPXQ+0/ZBe/faG5d1Szl9dD+yxEQArHPZ0K5zD1q370pOG9s0jyG9JX//Sy6X8/TxQ65dOs/lC2e5f9vju3ODFpbZqOHYiNoNmlHBoQbaOkk1b8uYEuLj2bFxBZtWLSAxPh4dPX2ceg6lRtteaGmLotx/6u7pQ+yZNxYUckwLVyV364lItTPX9mJZXDR+J5YT6nVevFcShExCJH8i+ROETOPra/qrTfvPUrJsRQ1GlDZ83r5m44p5nD12gK//q63gUI1e/QZTx6mxWley0nvy97/Cw0K5etGd82dOcOn8GcLDQr/dZ2pmTi2nptRr3IpylaujnUkSJJ+3r5k7adi3rcA2hYrTfsw8cuYvouHIMr7H186xbco/KGQJGOcpg32HGRm22MvPyOKieDyvuXivJAiZhEj+RPInCJnGf5O/zFjk5cvnYDaumMfhPVu/rV45NmjCwKGjKVW2gkZiymjJ338lJCRw68YVzhx34+zJY3wO/vjtPous2anfpBUNmrenSInSGf68nEKh4NiBnSyeNZGYyHCkWtrU6dSPet0Go637+6quws+9vH+DDWP6Ik+IxdCmKHk7z0FL31jTYamMSP4EIXMRyZ9I/gQh0/j6mpZItTjofheb3Hk0HZJKJCYmcnDnJtYvm/OtB14tRyeGj5tKsRKlNRpbRk7+/ksmk3Hb4xonjxzg9HE3voR8/nZfnvyFaNSqI41bdiBr9hwajPLPBX8KYtG00Vw4fRSAHHkK0H7sAuyKlNRwZBnb+6eerB7eHVlsJPo58pGvy3y0jcw1HZZKiORPEDIXkfyJ5E8QMo2vr+mmbbswed4qTYejEi+ePGT2+CE8f6IsulC0RCnGT5uHQ7WaGo5MKbMkf/+VkJDAtUvuuO3fg/vp48TFxQLKqqkONR1p3q4bVWs7ZehtoedPHWHh1FGEfP6EVEuL2h36Ub/HP2IV8A98eP2c5f90JjEqFL2sduTrtgAdk7QptKROIvkThMwlrfKfzFldQRCEDKFL78GaDuGPJcTHs37pbHq0rMPzJw8xMTVjxoLlHD5zLd0kfpmVjo4Otes1ZPmG7dx8/JbZi1dTrqIDMpmMaxfOMHpAZ5rXKMH6pbMJ+uCn6XBTpW7D5rievkn9pm2Qy2Sc37WWpf1a4Of9WNOhZVg58xVm5Lr9mGXLQVywD6+2jiA+NOj3DxQEQcgERPInCILGZMuRU9Mh/BGft6/p3bY+m1ctRCaT0bBZK85d96RT976Zsi1BemZiakb7Lj3Ze+w8Z6970mfQMCwss/EpKIDNqxbSvGZJRg/ozO3rl8kAG16+Y25hyaxlm5i/ZgcWltkIfOvN8gGtOeey8lv1WCFlstvlxXmlKxbWtsR/+cCrbcOJC/mg6bAEQRDSnEj+BEEQUuHssYN0a16T5489MTUzZ/mGHazcuJOs2a00HdpfL2/+goybOodrni9Zvn47FatURy6Xc/ncCQZ3a06Hhg4c2r2V2JhoTYeaIrWdmrLnlAd1GjZHLkvk9JZlrBrcjo8+bzQdWoZkaW2L84o9ZLPLS0LYR15tG05ssI+mwxIEQUhTIvkTBEFIgcTERJbOnsCkYb2JjoqkYpXqnLh0m8bNW2s6NOF/6Orq0rhFG3YfPsOpK/fo0qs/hkbGvH35nHmTh9OkWjHWLJpJ8MdATYeabFksszJ35TZmLNmAgbEpPs8esqRPU2647cpwK5rpgXl2awYt202OPAVIjPjM620jif34TtNhCYIgpBmR/AmCICRTZEQYI/q0Z8+WNQD0/2cU2/efwDqnjYYjE36nQKEiTJu7lOueL5k4YwG2dvaEh35h29rFNK9ZkpnjBvPutbemw0wWiURCg+bt2HfagwpVapIQF8vBpVPYPL4vEV+CNR1ehmNqmY2By3aTM38REqO+8MplJDFBYjVVEITMSSR/giAIyRAU4E/fdg25efU8+gaGrNq8m9GTZmToSpJ/IxNTM3r2H4z7TS9Wb9lN2QqVSYiP59j+nbSrX5HRAzrz5OE9TYeZLFbWuVjpcpjhk+agravLM4+LLOrZiGc3L2o6tAzH2NyCgUt3YlOoOLLoMF67jCQm8JWmwxIEQVA5kfwJgiD8xvu3r+jbzonX3k/JbpUD16PnaNCkhabDEv6AlpYWTo1bsO/4BfYdv0i9hk0BuHzuBD1b1WVwtxbcv3VNw1H+nlQqpWPPQWx3u0i+gkWJ/PKZTWP74LZyJonxcZoOL0MxNDVnwOId2BUphSwmgtcuo4kOeKnpsARBEFRKJH+CIAi/8Nr7Gf07NCLwgx958hVg/4lLFC9ZRtNhCSpUtkIl1m7by+mr92nVvgtaWlrcvn6JAZ2a0L9jI+56XEn35+nyFyrGNrcLtOvWD4CrB7axfGBrgt6/1nBkGYuBiSn9FrmQu2gZZLERvNk+RiSAgiBkKiL5EwRB+Im3r17g3KUZIcEfKVKsBK5HzpHL1k7TYQlpJH/BwixYsYHzNx/TqXsfdHR1eXD7BoO6NGNAp8bcv31d0yH+kp6ePqOmLmDppn0Ym1vw4dUzlvVrzu1TB9J98pqeGBib0G/RVnIXEwmgIAiZj0j+BEEQkuDv+47B3VoQ8vkTRUuUYsfBU1hmy67psAQ1sLHLzYwFK7hw6zFdevX/lgQO6NiYwd1apPszgVVr12ffqRtUqFKT+NgY9s4by545o4iLjtJ0aBmGvpEJ/RaKBFAQhMxHJH+CIAj/IzTkM0N6tOZTUAAFChXFZd9xzLNYaDosQc2sc9owbe5SLtxSrgRq6+hw+/oleraqy+gBnXnz8rmmQ/yprNlzsGLbIQaMmIREKuXeWTeW9m9BwOsXmg4tw/ghAdwxhphAsY1WEISMTSR/giAI/xEXF8vIfh3xffeaXLZ2bNt3lCwWlpoOS9Ag65w2zFiwAvcbj2jdoQtSqZTL507QqVEVZo4bTFCAv6ZDTJKWlha9nEexbvdxsufIySefNywb0JLbJw9oOrQMQ9/IhL4LtmJXtLSyCMz20aINhCAIGZpI/gRBEP6lUCiYM2EIXg9uY2JqxpY9R7DKkVPTYQnphI1dbuYv38DJy3ep36gZcrmcY/t30saxPGsWzSQyIlzTISapTIUq7Dx2FYcajiTGx7F3/lhc540lPjZG06FlCAbGJvRbuA3bQiWQxYTzZscYYj+913RYgiAIqSKSP0EQhH/t2bqGU2770NLSYs2WPeQrUEjTIQnpUP6ChVmz1ZV9xy9SvlIV4mJj2LZ2MW3qluPQ7q0kJiZqOsQfmFtYsnTzvm/bQO+cOsCKQW0I9nun6dAyBANjE/otdsGmYDESo0J5vX00cZ/9NB2WIAhCionkTxAEAXh07xYr500BYML0+ThUr6XZgIR0r2yFSuw5co61W13Jk68AIZ8/MW/ycLo1q8Ht65c1Hd4PpFIpvZxHscrlMMZZLAl4/Zyl/Vvw+Lq7pkPLEAxNzOi3yAXrvIVIjAxRJoBfAjQdliAIQoqI5E8QhL9eeFgoE4f2RiaT0aRFW7r1GajpkIQMQiKRUK9RM05evsvkWYswNTPn1YunDO7WnDEDu+Dv+07TIf6gQpWauB6/SsmylYiNjGDrhP6c2rQYuUym6dDSPSOzLPRfsh2r3PlJCP/Em+2jiQ/7qOmwBEEQkk0kf4Ig/PUWTB1FUIAfufPkY9biVUgkEk2HJGQwOjo6dO87iAu3HtOt90C0tLS4dPY47etXYsOyOcTGRGs6xO9kz5GTdbuP0757fwDcd6xh87g+RIeHajawDMAkS1YGLN1B1ly5iQ8N5M2OMSREhmg6LEEQhGQRyZ8gCH+186eOcPbYAbS0tFi8ejPGxiaaDknIwMyzWDBlzmKOXbiFQ7VaxMfHsWnlAto3qMwV95OaDu872jo6jJwynxlLNqCjp8/z21dY1r+laAeRDKaW2RmwdCdZcuQi7rMfb3aMJTE6TNNhCYIg/JZI/gRBSJG1a9dSsmRJTE1NMTU1xcHBgVOnTmk6rFQJC/3CwqmjABgwZBSly1XUcERCZlGwcFG2HzjByk27yJEzFwF+Pozq34mR/ToQ4O+j6fC+06B5O7YePIe1jR2fP/iwwrkNDy9lzNe0OmWxysmAJTswtcxO7Me3vNk1HllclKbDEgRB+CWR/AmCkCI2NjbMmzePe/fucffuXerUqUPz5s158uSJpkNLsdULphHy+RP5CxVh0PBxmg5HyGQkEgkNm7bk7DVP+v8zCm0dHa6eP027+pXYvn45iQkJmg7xm4JFSuDidomKVWsRHxPN9qmDObV5CXK5XNOhpWtZc+Wm/5LtaBmaEfPBm7d7JiNPiNV0WIIgCD8lkj9BEFKkadOmNGrUiAIFClCwYEFmz56NsbExN2/e1HRoKfL00X2O7NsOwKyFK9HT09NwREJmZWhkxOhJMzh2/iYVq1QnLjaGVQum0q1FLZ48vKfp8L4xz2LBsi0H6NTbGQD37avZNnkgcdFiNetXctgXYMjy7Uj1DIl6/4h3+2cgl6WfxF4QBOG/RPInCEKqyWQyXF1diYqKwsHB4afXxcXFER4e/t2HJikUChbNGItCoaBF206Ur1RFo/EIf4cChYqw69Bp5i9fj1kWC149f0Kv1o4smTWe6KhITYcHgLa2NsMmzGbKgjVo6ejy5Jo7K53bEhIgetr9ik3B4gxctBWJth4RL2/j67YAhVxUTxUEIf0RyZ8gCCnm5eWFsbExenp6DBgwgMOHD1O0aNGfXj937lzMzMy+fdja2qox2h9dOH2Uxw/uYGCoXJERBHWRSCS07tCVs9ce0LxNRxQKBa5b19KxURVuX7+k6fC+adK6Exv2nMAymxUBb16wfEBL3nrd1XRY6VrekuXpM2ctEqk2oY8v4n9yJQqFQtNhCYIgfEckf4IgpFihQoXw9PTk1q1bDBw4kO7du/P06dOfXj9+/HjCwsK+ffj6+qox2u8lJiaydvFMAPoMGopVjpwai0X4e1lmzcbi1ZvZ4nqEnDa2BPj5MLhbC2aPH0JkRPqoGlmiTAW2Hb5AoWIliQwNYe3wrtw9c1jTYaVrhSvVpMvkJYCEz/eOE3hxq6ZDEgRB+I5I/gRBSDFdXV3y589PuXLlmDt3LqVKlWL58uU/vV5PT+9bddCvH5py+sg+fN6+IotlVnoPHKqxOAQBoEbtepy6co+uvQYAcGTfdjo0qMLNqxc0HJmSlXUuNrieorZTU2QJ8eyZM4pTmxaLFa1fKF2nMW1GKv/A9PHqbj55HNBwRIIgCP9PJH+CIPwxuVxOXFycpsP4LZlMxtY1iwHoO2iY6OknpAtGRsZMnbuE3W5nsbPPy8dAf4b0aMXcScOJiozQdHgYGBoxd5UL3QcMB5QN4XfOGEpCBnjNa4pDs4407DMSgA9n1xHy8JyGIxIEQVASyZ8gCCkyfvx4rly5wrt37/Dy8mL8+PFcunSJzp07azq037p09ji+715jZp6Fzj37aTocQfhORYdqHL9wi+59BgFweM9WOjepxoM7NzQcGUilUpxHT2XK/NVoaevgeeEE60Z0ITI0RNOhpVt1uwykRtteAPgeWUj4y1sajkgQBEEkf4IgpNDHjx/p1q0bhQoVom7duty5c4czZ85Qr149TYf2W7s2rwKga6/+GBkZazgaQfiRoZERk2cvYsfBU+SyteOD73sGdGzMqgXTSIiP13R4NGnTmZXbDmJgbMq7x/dZMag1n/zeajqsdEkikdB00HjK1WsBCjnv9s0gyu/nZ6MFQRDUQSR/giCkyObNm3n37h1xcXF8/PgRd3f3DJH4PXl4j8cP7qCjq0uXnv01HY4g/JJDtZocv3ibNh26olAo2L5+Gb3aOPL21QtNh0Z5hxpsO3gOaxs7Pvv7sGJQW949vq/psNIlqVRK+3HzKFyxBorEON7unkhssI+mwxIE4S8mkj9BEP4KB3ZuAqBx8zZkzW6l4WgE4fdMTEyZt3w9a7buwSyLBS+ePKJbs5oc2LVZ4wVX8uQvxJaD7hQpUYbosC+sHd4Fr6tnNRpTeqWlrUO3GauxK1IKWUwEb3aOIyEiWNNhCYLwl0pV8rd69Wrs7e3R19enUqVK3L59+5fXL1u2jEKFCmFgYICtrS3Dhw8nNjY2VQELgiCkVGREGO4n3QDo1L2vZoMRhBSq36g5py7foVotR+LiYlkwZSSjB3Qm9Itmz9tZZs3Out3HqVbHicT4OFymOHPDbZdGY0qv9AwM6T1vI1lt7EkI+8ibXROQxUZqOixBEP5C2il9wN69exkxYgTr1q2jUqVKLFu2DCcnJ168eEH27Nl/uH737t2MGzeOLVu2UKVKFby9venRowcSiYQlS5ao5EkIgiD8yrnjh4mLjSF/oSKUKV9R0+FkOFFRkbx784r3b9/wwc+HwA/+fPoYxJeQz4SHhxIVGUlsbAwJ8fHI5HIAtLW00NXTQ9/AEGMjY0zMzDE3z4Jl1mxks8qBlXVOcuayxcY2Nzly5kJLS0vDzzJ9y25lzZY9bmzbsJqFsydzxf0kXZpUY8bSjZStWFVjcRkYGrFg7S4WTBmJ214XDi6dQlhwIA16j0AikWgsrvTI2NySfou2sXJQGyKC3vBu33TydJ6DVEtH06EJgvAXSXHyt2TJEvr27UvPnj0BWLduHSdOnGDLli2MGzfuh+tv3LhB1apV6dSpEwD29vZ07NiRW7dE1StBENTjpNteAFq37yLekP5GTHQ0nvdu8+DuLbwe3uf5Ey98fd6l6Zw6urrY58lPvoKFKFCoCIWKFKdo8VLY5rYXP6//kEql9BrwD5WqVmdY/+68ff2SQZ2b0nfIOHoMGqmxBFpbW5vxs5eRLYc1G5fPw33HGsJDgmkzYiZa2il+m5GpWVrb0mf+ZpY7dyDy7QN8jyzCruU48XsuCILapOj/yvHx8dy7d4/x48d/u00qleLo6IiHh0eSj6lSpQo7d+7k9u3bVKxYkTdv3nDy5Em6du3603ni4uK+6xkWHh6ekjAFQRC+Cfrgx8O7HsrKe63aaTqcdEehUPDi6WMunD3J1UvueN67TUJCwg/XWVhmJW++/Nja5cY6Zy6sclhjmTUrZuZZMDY2wcDAEF1dHaT/JiCyxETi4uOJjooiKjKCsLBQQj5/5nPwJwIDAwjw98ffzxc/3/ckxMfz8sVTXr54yuljh7/NaWaehRKly1G6XAXKVqhMmfKVMDExVdv3Jr0qVqI0bueuM338CA7t3cn6ZXO4f/s6M5ZuxDLrjztw1EEikdB3yDiyZbdm7uTh3D6xj6iwELpOWY6Onr5GYkqvbAoWp8+ctWwY3YtQr/PommXHum5vTYclCMJfIkXJX3BwMDKZDCur74slWFlZ8fz58yQf06lTJ4KDg6lWrRoKhYLExEQGDBjAhAkTfjrP3LlzmT59ekpCEwRBSNKFM0cBKF+pCjmsc2k4mvRlzbIFXDx3Cp93b767PWcuGypUcqBMuQqUKFWGIsWKY2FhmSYxyGQy/Hze8/r1S7yfP+PZ08c8e+zF82dPCAv9wrVL7ly75A4o/9hYrGRpHKrVwqF6LSpUqoq+gUGaxJXeGRkZs2DFBhyq1WTymKHcuXGZLk2qM3v5ZspWqqaxuFp06I65hSUThvbiyTV3NozuSa85GzAwNtFYTOlRoQrVaT9mLnvnj+XjtT3omllhWb6JpsMSBOEvIFGkoGTYhw8fyJUrFzdu3MDBweHb7WPGjOHy5ctJbuW8dOkSHTp0YNasWVSqVIlXr14xdOhQ+vbty+TJk5OcJ6mVP1tbW8LCwjA1FX/1FYSMLjw8HDMzMy54+mCcxis5/Ts24sHtG0yauZAe/ZzTdK707HPwJyoVy42vL9jYgJ8f2Noq79PT16dm7brUrdeQmrXrkjtPXo1vQ4uPj+f50yfcv3ubu7c9uH3TA5/33/eT09PXp1KV6tRybEDd+o3JZWunoWg165X3c/7p04WXL54ilUoZOGoK3foN1ejP8P6tawzr24HYqEhyFShG34VbMMmSVWPxpFdntq3g7NblIJGSp+NMTAtUSvVYsrgoHs9rLt4rCUIm8fW9kqpf0ylK/uLj4zE0NOTAgQO0aNHi2+3du3cnNDSUI0eO/PCY6tWrU7lyZRYuXPjttp07d9KvXz8iIyORSn9fcDStnrwgCJqhruQvPCyU+uXzIpfLuXTnGTZ2udNsrvQsMjKCTauXsWrJ3O+Svy7dHenYpQf1GjTGyMhI02H+1gd/P25cu8zVyxe5cvE8AR/8v7u/SPGSODVuToMmLclfsLCGotSM6Kgopowditv+3QDUcGzEtEVrMTYx01hML548ZGC3lkSGhpDNNg/9F28ni1VOjcWTHikUClznjeHu6UNIdfTJ13MphtYFUjWWSP4EIXNJq/wnRa0edHV1KVeuHOfPn/92m1wu5/z589+tBP5XdHT0Dwne10Ppmu5TJAhC5nbr6gXkcjkFChX9KxO/uNhYNq1dTu0KRVm1ZO4P96/e6EKL1u0yROIHyu2obdp3ZvmaTdx/+oaLHveZNH0OlatUQyqV8uzxI5bNn0mD6mVpWKM8a5bOx/f9O02HrRaGRkYsXLmRWQtXoqOryxX3k3RvXpvXL55qLKZCxUqx7cA5rHPZ8sn3LasGt+OT39vfP/AvIpFIaDtqNgXKVUGeEMvbPZOID/+k6bAEQcjEUtznb8SIEWzcuBEXFxeePXvGwIEDiYqK+lb9s1u3bt8VhGnatClr167F1dWVt2/fcu7cOSZPnkzTpk1FaW9BENLUzWsXAKhe21HDkaiXQqHg7MkjOFUrw7xp4/kS8pnc9nk0HZZKSSQSihQtzuBho3A7dQGvV34sXb0RR6dG6Ojo8PLFU5bMm07tikVp37Qurju2EBEepumw05REIqFDt97sO3aenDa2+L5/Q8/Wjpw7cfj3D04jdnnysWHvaXLnLUDoxwBW/9OBD6+TrhHwt9LW0aX79NVY2RcgMeIzb3dPQhYXremwBEHIpFKc/LVv355FixYxZcoUSpcujaenJ6dPn/5WBMbHx4eAgIBv10+aNImRI0cyadIkihYtSu/evXFycmL9+vWqexaCIAhJuOtxBYCqNWprOBL1CfjgR/9ubRnUsyN+vu/JYZ2TJas2cOTMJU2HlqYsLbPSsUt3du5zw+ulMhGsXrMOEomEe7c9mDRqMA4l8zJmSD/u3fbI1DtPSpQuh9vZ61StUYfYmGgmDunJyvlTkclkGonHyjoX6/ecpGDREkSEBLNmaCd8nj3SSCzplYGJKX3mbULbyJzYoNe8PzgbhVwzPy9BEDK3FJ350xRx5k8QMhd1nPkL+uBH0+rF0dLS4p73B4z/gmqDRw/uZeq4YUSEh6Gjo8OgISMYMnIcRkZGBAd/oni+XN+d+QuL9ydr1myaDjtNBXzw5+C+PezdvZ2XL/5/xalg4WJ06tGHFm07ZdrfjcTERBbPmcrG1UsBcKjhyKzlmzAxNddIPOFhoQzr3ZbHD+6gZ2hM3wWbyVOivEZiSa98nj1kxeAOKBLjyVqxJbkaJr9IlTjzJwiZS7o48ycIgpBReN69CSiLgGTWN/dfxURHM25of0YM6klEeBhlylXA/dodxk+ZmWHO86UV65y5GDxsFFduPeTY2ct06NIdfQMDvJ8/Ydq44VQrXYBZk8fg8y7znUXT1tZm7JTZLFvngp6+AR5X3OnZypH3b15qJB5TM3NWbjtEuUrViIuOZMPonry6n3SP4L+VXZFSdJ20GIDg24cJvnNUwxEJgpDZiORPEIRM6bHnHQDKVUi6GFVm8cHfj/bN6nLAdQdSqZSR4yZx7OxlChUuqunQ0hWJREKFSg4sW72Rh8/fM3PeYvLlL0BkRDjbNqyibuXiOPfqyP07P7YsyuiatGzLvuPKc4A+b1/Rs1VdPK6c//0D04CRsQlLN++jUvU6xMdEs3Fsb17cuaaRWNKrUrUb0bDPSAD8T60i4vU9DUckCEJmIpI/QRAypWdengCUKFNOs4GkoSdenrRpWIOnXg+xsMzGPrdTjB4/BW1tbU2Hlq6ZmZvTd+A/XL3jxe6Dx6jt6IRCoeDMiSO0a1KbDs0cueR+OlOdCyxWojSHT1+lXEUHIiPCGd67LXtdNHP2Xt/AkEXrd1OtjhOJ8XFsmdCX57cuaySW9Kpul4GUd2oJCjnv9s8gNthH0yEJgpBJiORPEIRMRyaT4f3MC4ASpcpqOJq0cdvjGp1aOPExKJAixYpz5tINqtX8ewrbqIJUKqWOoxN7Dh7j8i1POnbpgY6ODndv3aBP51Y0c3TgzAk35HK5pkNVCcts2dl+4CStO3RBLpezeMZY5k8ZSWJiotpj0dPTZ/7qHdSs15jE+Hi2TBzAs5sX1R5HevW1BYR9iXLI46J4u2cyiTHhmg5LEIRMQCR/giBkOn4+b4mNiUbfwAD7vPk1HY7KeVy7TK+OzYmKjKBK9ZocOXUR27+wj6EqFSpclKWrN3D7kTcDBg/H0NCIZ48f4dyrE83qZp4kUE9Pj3nL1jN2ymwkEgkHd21mRJ/2REaoP7HQ0dVl7spt1HZqiiwhnq2TBvHUQySAX2nr6tFj5hqy5MhFfIg/7/fPRCFTf6IuCELmIpI/QRAynTfezwDIV6BQpusn+uDubfp3bUNsTAx16jVg1/6jmJqZaTqsTMM6Zy6mzZ7P3SevGDZqHMYmpjx/6oVzr060dKrG5fNnMvx2UIlEQl/n4azZsgd9A0NuXj1Pv/YNCPzgq/ZYtHV0mL18C3UaNkeWEM+2yYPECuB/mGTJSq85G5Dq6BP59gH+Z9ZqOiRBEDI4kfwJgpDpvHvtDUD+gkU0HIlqvXnlTd8urYiOjqJmbUe27NyHgYGBpsPKlCwsLBk3eQZ3HnkzfPR4jIyMefLIk96dWtKppVOmKAxTr1EzXI+cJVt2K169eEqv1vV48eSh2uPQ1tFh1tJN1GnQ7FsC+Pz2FbXHkV7lzFeY7tOWAfD5zhE+3zuu2YAEQcjQRPInCEKm4/vuNQB58xXQcCSqExb6hb5dWhP6JYQy5SqwZdd+9PX1NR1WppfFwoKxk6Zz28ubgf+MQE9fnzse12jXpDbOvTry7s0rTYf4R4qXKsvBU1coWLgYwR8D6d+xMR6X3dUeh7aODrOWbaZW/SYkxsezdeIAvO9dV3sc6VXxavVo2GcEAH4nVxL53kvDEQmCkFGJ5E8QhEzHz0fZs83OPq+GI1ENuVzOiEE9ef/2NTZ2udm+9/Bf379P3SwtszJ11jw87j+lU9eeSKVSzpw4QoPqZZk1aTRhoV80HWKq5bSxZe8xdxyq1SI6KpIRfdtz/MAutcfxdQtoDceGyiqg4/vx+uFttceRXtXtMojSdRqDXMb7fdOJDwvSdEiCIGRAEkUGOLyQVh3uBUHQjK+v6QuePhibqP413bRacYIC/Nh/4hJlyldU+fjqtmbZApbMnYa+gQHHz16meMnSKR4jOPgTxfPlwtcXbGzAzw/C4v3JmjWbSmNVKBQEfPDnzetX+Pq8JzDAn08fP/Il5DMRERHEREeTkBCPQqFAKpWio6OLgaEBJiammJqZY5k1K9mz58A6Vy5sbe2ws8+bLhPd58+eMGPyeC6cOw1AFgtLho2dTIeuvTPsOdP4+HjGDx/IkQN7ABg4cjI9Bo5AIpGoN464OMYM7MKNy+fQMzCi/2IXchcro9YY0qu4mGhWDW7Ph1dPMbAuQP6ey5Dq6AEgi4vi8bzm4r2SIGQSaZX/iORPEAS1S8vkLzExkWpFsiOXy7n+8BVWOXKqdHx18/K8R5tGtZDJZCxdvZGOXbqnapy0Sv6Cgz/hce0Kd+/c4uH9uzx5/IiIcNVWjsxhnZMCBQtTuGgxihYvSclSpSlUpFi66Gd46fw5pk4czYtnTwEoUqwE0+Yto1xFBw1HljpyuZxFs6eyYdViANp168eIyfOQStW7USg2NoaRfTtw58Zl9I1NGLh0JzYFi6s1hvQqJNCfeT2bIosOw7xEXexajkMikYjkTxAyGZH8ieRPEDKNtEz+PgUF0LhKEaRSKc/8wjLsKgxAXFwczetV4dWLZzRv1ZZ1W3amehVGVcmfQqHg2RMvjh89jPvpkzx6+OCHa7S0tLDPkxe73PbksrEle/bsZLGwxNTMDEMDQ3R0dZFKpcjlcuLj4oiOiSYiPJzQ0C8Ef/pEUGAAH/z98fF5R+iXpLdTGhgYUKpMOSpUcsChWg0qVa6KkbFxqr43fyoxMRGXLRtYMHv6t+2frTt0Yczk2ViqeGVVXVw2rmHW5NEoFArqNW7FtEXr0NHVVWsMMdFRDOnRmof3bmJkZsGgFbvJYZ95zvH+iVcPbrJ2eFdQyMlZfwDZHNqI5E8QMhmR/InkTxAyjbRM/p4/9qRb81pky26Fh9dblY6tbisXz2H5gllkzZadK7cfYmFhmeqx/jT5+/w5mL27trN39/Zvq1xfFS1WgspVqlK+QiVKlipN/oKF0FVRohD65QuvXnnz/OlTnj7x4rHXQx56PvhhdVFbW5tyFSpRs44jdes1pESp0mpfrfr8OZg50yaxa/sWAMzMszB60kzade6h9lhU4fjh/Yz6pw+JCQlUrl6X+Wu2Y2Co3i24kRFhOHdtwTOvB5hmtWLwSlcsc9qpNYb06uqBbbitnAkSKXm7zscwZ0GR/AlCJiKSP5H8CUKmkZbJn8eV8wzt2ZrCRUtw/GLGLcfv5/Mep+pliIuNZe3m7bRs0+GPxktt8vf6lTerly3m4L7dxMXFAcpG4Y71G9CoSXPq1nMiu5XVH8WWUnK5nJfeL7hz6yYeN65x49oV3r/7PtHPYZ2T+g0a06hpC6rWqIWOjo7a4rt35xZjhjvzxOsRABUcqjF70Sry5i+othhU5eoldwb26EBsTDQlylRk6eZ9mJqZqzWG0C8hDOzUhNfeT7GwtmXwqr2YZVXv71x6pFAo2DNnFPfOuqFlaEa+7ovwXttXvFcShEwirfKfjPenSEEQhF8I/3fbnXkWCw1H8mcWzZ5CXGwsVavXokXr9mqf39fnPYP796R6hZLs3rGVuLg4SpUuy5KVa3n+xp8drgfp2KWb2hM/AKlUSqHCRejSvSer12/mwZOX3H/szZKVa2nctDnGxsYEBnxg+9aNdGjVmJIFbBk1ZCDXr15GLpeneXzlKlTizKWbTJu9AENDI+54XKNx7YqsWbaAhISENJ9flarXcmTHgZOYmJrh9eA2Azo15nPwR7XGYJ7FgpUuh7Cxy0NIgC8bRnUnOjxUrTGkRxKJhLajZpOrQDFk0WH4HJ6n6ZAEQcgARPInCEKKzJ07lwoVKmBiYkL27Nlp0aIFL1680HRY30T8+6bQzNxco3H8iSdenhx3249EImH6nAVqrbYYExPDgjnTqVa+OAdcdyGXy2nQqAkn3S9z4dotevTqmy6/t/Z58tKjV192uB7kpU8Q+w4fp3uvvmTNmo0vX0LY6bKZ1k3qUaFkQebNnMK7N6/TNB5tbW0GDB7G5Vue1KnXgIT4eJbMnUbrhjV49uRRms6tamXKV8T1yDllM/jnT+jfoRFBH/zUGkPW7DlYuf0w2aysCXz7ko1jexMXHaXWGNIjHT19esxcg5aBCbGBafs7LQhC5iCSP0EQUuTy5cs4Oztz8+ZNzp07R0JCAvXr1ycqKn28EYuKigTAyNhEw5Gk3oqFswFo2aZ9qto6pNadWx7UrVqOJfNnExcXR/UatTh/9Sa797tR2aGq2kv+p9bXbalLV67l6WtfDh8/Q5fuvTA1M8Pf14dli+ZRuUwR2jZrwNHDB9J0Nc7WLje79h9h5fotmJln4anXQ1o5VWf1knkkJiam2byqVqhocfYcdSenjS0+b1/Rr0ND/H3eqTWGXLb2rNh2CENTc3yeeuIy1ZnEhHi1xpAeWVjb0HvmSk2HIQhCBiGSP0EQUuT06dP06NGDYsWKUapUKbZt24aPjw/37t3TdGgAxP67GmBgaKjhSFLH+9kTzp85gUQiYcTYiWqZUyaTsWjeTJo3qM2b16+wts7J1p17cTt5jjJly6slhrSira1Nzdp1WbFmA8/f+LPJZTd1HOsjkUi4evkC/Xp0onzx/CyaN5NPH9OmabZEIqFthy5cvf2Qhk2akZCQwNL5M2jXuDZvXnmnyZxpwT5PPlyPuGOfNz8B/r7069CQ929eqjWGfAWLsGrrAXT1DXhx+yp75oxWy1be9K5Qher8s/qApsMQBCEDEMmfIAh/JCwsDAALi5+fsYuLiyM8PPy7j7QSFxsLgL6+QZrNkZa2rFsBQONmLclfoFCazxcWGkqXts1ZNHcmcrmc9h27cOPuI5q3bJ1hVvqSS19fn1Zt2nHgyEk8n75i5NgJZM9uRVBgAIvmzqRcsXwMc+7L82dP0mT+7FY52LJzP6s3bsPUzJxHnvdo5ujAzq3ryQC11wDIaWPLbrcz5C9UhE9BAfTv2JjX3s/UGkPx0uVZuHYnUi1tPC8c5+jq2Rnm+5eWcuTJr+kQBEHIAETyJwhCqsnlcoYNG0bVqlUpXvznDZjnzp2LmZnZtw9bW9s0iynh321g6qzuqCpfQj5z9PA+APo7D03z+T74+9Gkfg0unj+LgYEBazduY+2mbenyTJ+q2drlZuKUGTx68ZaNW3dSvmIl4uPjcd3pQq3KZejWoSV3b99U+bwSiYTW7TpxyeM+NWrVJTYmhmnjhtOvS2s+f1JvIZXUym5lza5DpylctAQhwR8Z1Lkpr16kTcL8Mw416jJt4RpA2fLg4p4Nap1fEAQhoxLJnyAIqebs7Mzjx49xdXX95XXjx48nLCzs24evr2+axSSTyQDQzoDJn9v+PcTHxVG8RCnKV6yc5vN1bdeCly+eY50zF6fPX6V9py5pPmd6o6urS+t2HTh78TqnL1ylSfOWSCQSzp46QZN6NWjT1AmP61dVPm/OXDa4Hj7BzHmL0dXT46L7aRrXrsi1y+dVPldasMyajR0HT1KsZGm+hAQzqEszXj5/rNYYGjRvx9AJswA4sX4B9866qXV+QRCEjEgkf4IgpMrgwYM5fvw4Fy9exMbG5pfX6unpYWpq+t1HWvm6/SsjNtU+tG8nAJ2691LLlsugwAAKFi7C2UvXKVGqdJrPl95VrOTA9t37ufXgCZ279URbW5trVy7SslFd2jZroPKVQKlUSt+B/3Dm4g0KFSlK8KeP9GzfjIWzpmSIlhBZLCzZvv8EJUqXJTTkM85dm6s9AezcezCdew8GwHXeWLzvXlfr/IIgCBlNxnt3JAiCRikUCgYPHszhw4e5cOECefLk0XRIScpoZ4BeeT/n2eNH6Ojo0FJNff0KFirM8dMXyJXr18n73yZ/gYKsXLuRe14v6NmnPzo6Oly9fIEm9WrQrUNLnj1VbYJTpFgJTl/0oFuvfigUCtavXESXVg0IUHM7hdQwM8+Cy77jlCxd7lsC+PrFU7XG8M+4GdRv0hq5LJFtkwfx4fVztc4vCIKQkYjkTxCEFHF2dmbnzp3s3r0bExMTAgMDCQwMJCYmRtOhAf+/4if/d/tnRnH6+GEAatR2JMsviueo0tYde8maLZta5sqIbO1ys3j5au4+ek6X7r3Q0tLi7KkT1K1anmHOfQkM+KCyuQwMDFiwdBUbXfZgbGLKvdseNKvrwNVL7iqbI62Ympmzbd8xipcq8y0BfPtKfb0/pVIpUxasoWylqsRFR7JxTC++fFTdz0YQBCEzEcmfIAgpsnbtWsLCwqhVqxbW1tbfPvbu3avp0ID/P+uXEbbN/Zf76eMANG7aQm1zZsueXW1zZWS2drlZsWYDN+4+olnL1sjlclx3uuBQtiiL588iOjpaZXM1bdEa9yu3KFGyNF9CPtOrQ3NWLp6T7tsZmJqZs23vMYqWKEXI508M6tIMn7fqazquq6fHgrW7yJO/EOHBQWwe15fYqAi1zS8IgpBRiORPEIQUUSgUSX706NFD06EBoKurB/x/y4eMIPhjEI8fPgDA0alhmsxx8qhbmoz7NylQsBDbdu7lzMVrVKzsQEx0NAvnzKB6xZIcPXxAZVuN7fPm49i5K3Tt0QeFQsHyBbPo37UN4WGhKhk/rZhnsWDb3mMUKlKcz5+CcO7anA9+79U2v6mZOUs378Mia3YCXj9nx7QhyBIT1Ta/IAhCRiCSP0EQMpWv/f1iY9PHNtTkuHH1EgDFS5Qiu1UOlY8f8MGfmVPGq3zcv1WFipU55X6Fzdv3YGNrh7+vD/16dKJ9i0a8eqma7Y76+vosXL6G5Ws3oaevz0X307R0qo73c/Wep0spC8usuOw7Rr4ChQgK8MO5a3M+BQWobf6cNrlZsnEvOnr6PL99BbcVMzLc+V9BEIS0JJI/QRAyFQMjIwCio6I0HEny3bpxBYCqNWunyfgTRw8jIiI8Tcb+W0kkElq2bsvN+48ZPX4Senp6XLl0ntoOZZk/exqxKlp5bt+pG8fPXsbGLjfv376mbaNanDt5VCVjp5Ws2a1w2X8c29x58Pd5x+DuLQkN+ay2+YuWLMOc5ZuRSCTcOLKLqwe2qW1uQRCE9E4kf4IgZCqGRiYARESEaTiS5Lt3R9lCoLJDVZWPfcH9DCePH0FbW1vlYwtgaGjI+EnT8LjnRT2nhiQkJLB0wRzqVCnL9auXVTJHiVJlOHPJg6rVaxEVFcnAnh1YvWReul7RymGdi+37T2BlnZO3L58ztFcbItX4B4ia9RozZNwMAI6umcNTj4tqm1sQBCE9E8mfIAiZiqmZGQAR4RljpSsyMoLX3srS9OUqVFLp2DKZjOmTxgLQtUdvlY4tfM8+T15cDx5l68695MhhzZvXr2jdpB6jhw5Sye+ipWVWXA+foFe/QQAsnT+D4QN6EJtOquwmxTa3Pdv3n8DcwpJnXg8Y1b8jcXHqO4vbqfdgmrfrhkIuZ+f0oQS8Vl8FUkEQhPRKJH+CIGQqpmZZAAj9EqLhSJLn2eNHKBQKrHPmUvl5v0P79/Di2VPMzbPg/M9wlY4t/EgikdC8ZWtu3n9Mj979ANixbRO1HMpw+cKft2zQ0dFhzsJlLFy2Bm1tbY677adzqwZ8/vTxj8dOK/kKFGLb3qMYGZtw/9Z1Jg7pRaKairBIJBLGTF9EucrViYuJYsuEfkSGqm/7qSAIQnokkj9BEDIVcwtLAELUeMboT7x4pmwYXrR4SZWOK5fLWbF4PgD/DBv5bUVUSHumZmYsWbGGo6fcsc+TF38/X9q3bMTYEf8QpYKzqF179sH18EnMzLPw8P4dWjesycsXz1QQedooXrIMG3YcQFdXjyvuJ5k7aZjatqzq6Ooyd5ULNnZ5CAn0w2WyM4kJ8WqZWxAEIT0SyZ8gCJlKFktl0/LQkM9qW2H4E6+9lVvRChUuotJx3c+c5KX3C0zNzOjdf5BKxxaSp1qNWly99YC+A5wBcNm8HsdqFbh/745Kxj55/ir2efLh5/ue9k3rcvP6lT8eN61UqlKd5Ru2I5VKObZ/J2sXz1Tb3OZZLFi80RU9Q2PePLrD4WXT0vV5SUEQhLQkkj9BEDIV8yyWaGlpoVAoCP4UpOlwfuvd21cA5C9QSKXjbtmwFoDuPftgamqq0rGF5DMyMmL+4uUcOnaanLlsePvmFU3r1WDZwrnIZLI/Gjtf/oKcOH+VipWrEB4WSs8OzTh+eL+KIle9eg2bMmvRKgC2rV3CXpf1aps7T/5CzFuxBYlEws3je7nhtkttcwuCIKQnovybIAiZipaWFpbZrPgY+IGPgQHksM6l6ZB+yc9H2QTbzj6Pysb09XnP5YvKM2Y9+/RX2bhpKTExkZfeL3j29Alv37zC38+PTx+DCA39QnRUNAkJCQDo6upgaGSEuXkWLLNmI4e1Nba2ucmbLx8FChbGMmtWDT+TpNWq48i1Ww8YOcyZwwf2MW/WVK5cvsCajS7ksM6Z6nEtLbOy1+0U//TvyfEjhxg2oDtBQQH0HjBEhdGrTrvOPfgUFMjS+TNYMnMc2axyUKdBc7XMXbV2fZxHT2PVgqm4rZxJjjwFyFdatUWWBEEQ0juR/AmCkOlkz5GTj4EfCPjgR8ky5TUdzk8pFAoCPvgBYGNjq7JxD+3bg0KhoHqNWtjnyauycVVJoVDwxOsRZ8+c5MrFC9y9c4vo6Og/Hjd7ditKli5DmXLlqVjJgQqVHNLNyqd5lixs2rYLx3oNGD3iH25cvUydquVZvWEbtR3rp3pcAwMDNmzbzZTxo9i0bhVzp44j+GMQYybPQiKRqPAZqMag4WMJCvzAbpdNTBneD4us2Sld3kEtc3ftNwTvZ16cPXaA7VMHM2zDEbJYpT75FgRByGhE8icIQqZjldOGx553+eDnp+lQfikiPOxbqX6rP1j9+V9H3Q4A0KZDJ5WNqSqBAQHs3L6Fvbt38vrVy+/uMzY2pmjxEuTPXwBbu9zksM6BuXkWjIyN0dHWASA+Po7IyEjCwkL5GPSRgA/++Lx/x+tXr/Dxec/Hj0G4nz2N+9nTgHIluHTZctSq40j9Bo0oV74iUqnmTjxIJBI6dulGhUqV6d2tE16PPOnYugnDRo1j9ISpaGlppWpcqVTKzHmLscphzexpE9m4eilfPgcza/HqdNfjUSKRMHXuUoICAzh/5gSj+ndi8/6z5M5bQC1zT5q7gvdvvHnx5BHbJg9k8Mp96OjppfncgiAI6UH6+hdBEARBBaxz2QHg5/NOs4H8xufgTwAYGRtjYGCgkjF93r/jidcjpFIpjRo3U8mYqvDm9SsWL5jLgb27v23h1NfXp3ZdRxzrN6BqteoULlL0jxKzyMhInj55jOeD+9y9fYubHjd49/YN9+7c5t6d2yyeP4ds2bLTqGlzmrdsTfWatVOdbP2p/AUKcubiNSaNG8WWjetYtmge9+7cZu2WHWTNmi1VY0okEv4ZPpqs2bIz8p/+HHDdQXh4GEvXuaCXzpIbLS0tlq1zoUvrhjy8f4dhvduy5YA7WSzTftuuvoEhC9bupGPTmvi9eMzBJZNpP25+ulwlFQRBUDVR8EUQhEwnl509AD7v32o2kN8IC/0CQJZ/21OowkX3swBUrOyQLs6/hYWGMm7UMCqXLc6enS4kJCRQqXIV1m3aymvfQPYePELf/gMpWqz4H6/IGRsbU7FSZfoNGMSGLS48evaSJ95vWbN+E63atMXMzIxPnz7ismUjrZo2oHiB3EwcO5Knj71U9GxTRl9fn0XLVrFhyw4MDA25evkCTjUr43n/3h+N27FLd7bs3Ieunh5nTx6lX9c2RKugxYSqGRgasmH7fmzt7PH3eceo/p2IjVVP03rrXHYsWLkViVTKndMH8Ti6Ry3zCoIgaJpI/gRByHRscyvPub1/+1rDkfxaREQ4gErPpF29fAGA2nXrqWzM1Dp3+iQO5UqwYe0qEhMTcazvxPkrNzh36SqdunTDxMQkzWOwtbOjS/eebNvpyhu/INyOn6ZHrz5YWFoSFBTI2lXLqVapDPVqVWH3DhdiYtSTfPxXm/Ydcb/sQf4CBfH386V5g1rs27Pjj8Zs0LgZu/YdwdDQiOuXz9OrY/Nvv2/piWW27GzafRgTUzO8Htxm5hhntbVhqFi1Fs6jpgLgtmIG7596qmVeQRAETRLJnyAImY5dnnwA+L5/m657/cVEK1djDA2NVDKeQqHg9s0bAFSrXlMlY6ZGYmIiUyaMoX3rZgQGBpC/QEGOnDjDoaMnqVBRc9UVdXR0qONYjxVr1vPynT+uBw7TrEVLtLW1uXfnNoMH9KZEIXtmT59MYECAWmMrUrQY7pc9aNCoCXFxcQwZ0JupE8f8UTuI6rXqsO/IKUxMzbh76wY92jYhPCxUdUGrSL4ChViz1RUtbW3OnTjExuVz1TZ3135DqO3UFFliAtunDiYy9LPa5hYEQdAEkfwJgpDpZM+RC30DQxISEvBNx1s/42LjANDT01fJeP5+vnwMCkRbW5vSZTVT5TQyMpJObVuwavkSAAY4/8P12/epXddRI/H8jI6ODo2aNGOn6wGev/Zh6ozZ2NraEfL5M4sXzKV00XwMGzyAt2/Ut3psambGzr2HGDl2AgDrVy2jW4dWRISnfsWufMXKHDx2liwWljx8cJeubRoR+iVEVSGrjEO1msxauBKATSsXcOboAbXMK5FImDx/NXZ58hP6MYBdM0cg/8P+i4IgCOmZSP4EQch0pFIp9v9WDnz14pmGo/m5RJlyVVJHR0cl43k9fABA4SLFVFZAJiUiIiJo07wh7mdPY2BggMsuVxYsXqaRWFIiu5UVI8eM4+Gzl+zYs49KlasQHx/P9q2bqFCqCIP69uTN61dqiUUqlTJxygw2b9+Dvr4+58+eoqlTTfx8fVI9ZsnSZTh47AwWltl48siTbm0bp8sEsG2n7vR1Hg7ArHGDefLwz84+JpexiSnzV29HV98A77vXOLd9lVrmFQRB0ASR/AmCkCnlKVAYAO/nTzUcyS+o+GzT82dPACheoqRKx02O2NhYOrdrwe2bHpiZm3PstDstW7dVexx/Qltbm+YtW3Pu0lXOnL9MPacGyOVyXHfvoFKZYgwbPIAPH/zVEkvL1m05fvYiOXJY8/zpExrVrcbDB/dTPV7R4iU5dOIsllmz89TrId3aNv5WcCg9GTVxBnXqNyIuLpbRAzrzMfCDWubNV6goE2YtBeCcy0pe3LmmlnkFQRDUTSR/giBkSvkLFQPg+bPHGo7k5yT/VreUy+UqGe/1S28AChYqrJLxkkuhUDB88ACuXbmMsYkJR0+epWKlymqNQdUcqlbj4JETXLx2k3pODZDJZMqVwJKFmT19MhEREWkeQ9lyFTh7+QZFi5XgY1AgLRvXxf3sqVSPV7hIMQ6dOIuFZTaeej2kR/um6e4MoJaWFkvWbqVAoaIEfwxkzMAuxMXFqmXuRi070KJ9dxQKBbtnDScsOEgt8wqCIKiTSP4EQciUChQpDsCzx480HMnP6ejoApCQmKCS8d69fQOAfd58KhkvubZt3sDePTvR0tJil+sBypQtp9Lxv3z5wpVLF9m4fi0Tx42mT4+utGnRhEb16uBUpyaN69elTYsm9OnRlQljR7FqxTJOHDvCS+8Xf1zwp1z5Chw8coKzF65Q2aEqMTExLF4wl4qlirB7h4vKEvefsbGx5aT7ZWrVcSQ6KoruHVqxZ6dLqscrVLgoB4+fIYtlVrw879O7U0siI9M+kU0JY2MT1m/fj6l5Fp4+us/cicPUVgF0xJR5FChSnMjQEHbNHC7O/wmCkOmIJu+CIGRKhYoqtz6+e/OKiIhwTExU105BVb423o5VUXsBfz9fQNneQF1evfRm4tiRAMyYPU8lhV3kcjm3PG5w7KgbF9zP8fRJ6ldv9fX1KVGqNOUrVKRqtepUrV4TS8uU91WsXKUqZy5c5vhRNyaNH8vbN68ZPKA3Lls3smjpKkqUKp3qGH/H1NSUvYeOMXRQP1x372C4c1+CPwYxePjoVDUmL1K0OPvdTtK6qRMP7t6if9e2bN59GP10dDbTzj4PqzbupEf7ppw87ErhYqXo0HNgms+rr2/AnJXb6NK0Jq89b3HWZSUNeg1L83kFQRDURaJQ15/T/kB4eDhmZmaEhYWptB+WIAia8fU1fcHTB+M0TMqaVitOUIAfuw6foVKV6mk2T2p5XL1E1zaNKFi4CFduPfyjseRyOXbZjElMTMTL+x25ctl8d3/wp08UtLfG1xdsbMDPD2JkAWTNli3VcyoUCpo3cuTalcvUruvI4WOn/qhRe2hoKFs3bWDrpg28e/d9ldbcue0pVrwEefLmJWfOXGSxsMDIyAgtLS0SExOJjoriy5cvBAUF4u/nx+vXr/B+8Zzo6OjvxpFIJJQpVx6nBo1o2rwFxYqXSHECFRcXx7rVK5k/ZyaRkZFIpVIGOA9h/OTpGBmppm1HUhQKBTOmTGD5koUA9B88jGmz5qcqAQR4cO8ubZo5ERUZQW3HBqze6oqurq4qQ/5jW9atZM7UsWhpabFquxvlKqvndXz6yD6mjOiHRCJhwNKd5C+T/rcxx0ZFMLFRafFeSRAyibTKf0TyJwiC2qkr+RszsAuXzh5n3NQ59Bk0LM3mSS0vz3u0dKqOdc5cPHj2Zy0pQr98obC9FQABIVHfVhW/Sovk76jbIXp0boe+vj53PJ+Q294+VePExsayavlSli9ZSFhYGKBc7WrctDkNGzWmeo1aZM+ePcXjyuVyXr96xb17d7jlcYOrV6/w7OmT767JX6Agbdt3pEOnLuTJmzdF43/w92f8mBEcPqhsS2CX255lq9ZRq07atrVYvWIpk8ePBqBT154sXL4GLS2tVI3lcf0qHVs3ITYmhqYt27F4zZY/SuBVTaFQMNK5N0cPupLFIivbj17GyjqXWuaeOW4wx/bvxDSrFSM3H8fY3EIt86aWSP4EIXNJq/wn/fwfXhAEQcWKlVKePfO8f0fDkSTN7N83k6ooux/2b+EOfX39HxK/tCCTyZg9YwoAQ4aPSnXid+PaVSqXK8WMqZMICwujSNFirN2wmdfvP7Bpiwut27RLVeIHyrYJBQoWpEPHzixdsZq7D7x49daPNes30bhJM/T09Hj10pu5s6ZTqmgBGtevy8H9e4mPj0/W+Dlz5cJl1172ux3D1tYOn/fvaNW0ASOGDErTgjDOQ4azat1mpFIpu3dsxblvdxISUndu1KFqdTbv2Iu2tjbHDu9j+oQRajtflxwSiYTZi1ZRpFgJvoQEM/6fHiQk8+fzp0ZNmY99voKEBwexd/64dPV9EQRBSC2R/AmCkGkVL61sdO5577aGI0maRdasAMTExBAVFfVHY0VHRQLKYhm/sn49TJum/Pz8WerbYJw4doSXL55jniULQ4aPTPHjFQoFi+bPpVH9Orx5/QrrnDnZvG0Ht+89pFv3nhgaGqY6tl+xzpmT7j16se+gG+/9P7Jxiwt1HesjkUi4euUSPbt2onihvCyaP5cXL55zcP9eXLZs4uD+vXwMSrr6o1ODRty8/4g+/ZVn0rZt3kBNh3Lc9LieJs8BoFPX7mzevgcdHR3cDu6jX4+OyU5a/1fdeg1YtX4rEomEXVs3sGrJXBVH+2cMDA1ZvcUVE1MzHj+4w7I5E9U0rxGzlm9GW1eXpzfOc/3wDrXMKwiCkJZE8icIQqZVtGRZtLS0CPzgz4d/i6GkJ0ZGxt+KbAR//LOy8nFxyjf+evr6P9x3wf0sHdo0A2DWLJg+Xfm5WcO6NHSswQX3symeb8PalQD06TcwxdtREhMTGdi3FzOmTkIul9O5a3fueT6hQ8fOat1yaGJiQqfOXTl64jTPvN8yfuJkrHLkIDAggBlTJ1GpTDF6du3EP4P607NrJ4rkt6NXt048eeyV5FhLlq/i+Gl3bG3tePf2DU3q12be7Ol/XHH0Z5q3bM0O1wPo6elx6vhRendtR1xcXKrGatGmPbMXLgNg+YJZuO7YosJI/5ydfR6WrFHGtH/HRs4cPaCWeQsWKcHQcTMBOLZ2LgFvXqhlXkEQhLQikj9BEDItA0MjCv5b9fPurRsajuZHEomE7FbWAAQE/Fkza7lcWZL+f89+bdu8gbYtGvPm1V2GD4d798DXV/l5+HB48cyDti0as23zhmTP9frVS25cu4pUKqVPvwEpilMmk9G3Zzd279yOlpYWK1evY8OmrZiZmaVoHFWztbNj0pTprF67ET09HeztYdEi+PgRZDLl5/nzE3lw7yB1a1TG/dyZJMepUas2N+560qFTF+RyOQvmzKRZw7r4+/ulSdz1GzRm177D6Ovrc+70SXp3bZ/qBLBX34EMHz0egCljhnDh7ElVhvrHatdryKBhYwCYM3Eo7157q2Xedt36UbVWfRLj49k1czgJqfz+CoIgpAci+RMEIcWuXLlC06ZNyZkzJxKJBDc3N02H9FOlyiur9N25eU3DkSTNOqeyKqe/n49KxvvvuaQL7mcZOdSZ0qXh+XMFS5ZA2bLKgi9ly8KSJcrbS5eGkUOdk70CePjgPgBq13UkZ66UFd+YOG40B/fvRUdHhz17D9KrT78UPT4tPX7sRbfObXF0TOTJE2VynC0bSKXKz8OHw6NHidSuHUeX9q2SXAEEMDMzY8MWFza77MTYxISbN65T06Ec53+SMP6pOo712XPgCPr6+rifOflHW0DHTJxGhy7dkcvlDO3XDS/PeyqO9s8MHTOZylVrEhMdxTjn7sTGRP/+QX9IIpEwaf4qLCyzEfDmBSc3LkrzOQVBENKKSP4EQUixqKgoSpUqxerVqzUdym+Vq1QNgNse6TP5s/m3J5/v+/d/NI6WlrJt63+3GC6cNwszMzh1SoGVVdKPs7JS3m9mBnNnTSP406fffhw9fBCAevUbJOv6rx9bNm5gzcrlACxZvoqKlR349OlTuvmYPWMq1tYJ7Nun4GdHDg0NYd8+BTlyxLNk4bxf/kzatu/I1Zt3KV2mLCGfP9OuZRMWzJ2ZJo3ha9auy+79bujr63Pm5HEG9emWqu2mEomEhcvWUKtOPWJiounbpTX+vqr5w4QqaGlpsXTdVrJlt+LNy2csnDZaLfNaZs3OxHnKrc5X9m/B+17anecUBEFIS6LVgyAIf0QikXD48GFatGiR7Meoq9UDQHhYKPXK5UGhUODh9YZs2XOk6XwptXLxHJYvmEWHLt1Ztnpjqsd58fwpNSuVxsLSklc+QTx+9JAaDuUYPly5wvc7w4fDsmWpnj5TkEhg8WLl9+J3liyB0aMlnDl/hUoOVX55bWxsLONGDWfLJuXW2oaNm7J2k0ua/Ht2/twZOrdrSXx8PG06dGbF2s2pOkcZER5Oi0Z1eOL1iAKFirLv+HlMTDW7Nfe/PK5dpnvbxsjlcqYvXk/DFu3VMu+8ySM4tHsLZtlyMGrrSQxN0s/3RLR6EITMJa3yH22VjSQIgvATcXFx351DCg8PV9vcpmbmFCxaghdPHnHjyiWat+mgtrmTI0/eAgC8efXyj8YxNFQ2F4+KVFb9vHTxPABduiTv8V26KJO/yZOhX/rZiak2R4+Cs3PKvl8jRypo4FiLMeMnMXLMuJ82SNfX12fZqrVUqFiJYf8M4tSJY9SvXZU9+93IkzefCp8F1K3nxJYdrnTv1JYDrrswNjZh7qLlKW4Eb2Jqyo69bjSqW42XL54ypF9XNu48hLZ2+njb4FCtJoNHjmfFwtnMmzyCYqXKY5dHtd/LpAwdP5M7Ny7j++41h5ZNo8vkpWk+pyAIgiqlatvn6tWrsbe3R19fn0qVKnH79q/LqIeGhuLs7Iy1tTV6enoULFiQkyfT10FyQRDSzty5czEzM/v2YWtrq9b5K1SpBcD1KxfUOm9y5MmvTP5evnj+R+OYmZkDykQ7JiaGyEhln7nktsj7ep1UqjwT+Ld9fM3b/u2+8Vtfr5PJZMydNZ0aDhXwfHD/l4/p3K0Hp89fJmeuXHg/f4ZjTQduXLuSvAlToFGTZqzb5IJEImHbpnUsmD0tVePkzGXDdtfDGBgYcvWiO3OmjFVtoH/Iefg4KlapTkx0FJOG9iJeDYVYDAyNmL54PRKplAfuR3l4UbyXEQQhY0nxn/D27t3LiBEjWLduHZUqVWLZsmU4OTnx4sWLJBvxxsfHU69ePbJnz86BAwfIlSsX79+/x9zcXBXxC4KQAYwfP54RI0Z8+zo8PFytCWDl6nXYuXEF1y+fR6FQpHgVJC3ly18IiUTCly8hfPoYRLbsPzmc9xsmpqZoa2uTmJjI58/B3/r9ffyoTG5+5+NH5We5HPzSpjBluva1PkpwsLK4y+8EBys/Dxo8hH179/D0yWPqVHdg7ITJjBwz7qcrZOXKV+DStVt0aNuS+3fv0KppA1au3UTbDp1U9EyUWrfrQHh4GCOHOrN04Vwss2WnT3/nFI9TsnQZVm3YSu+u7dm+eS0FixSjQ9deKo01tbS0tFiyZguNa1fi+ZOHrF08k6ETZqX5vMVLl6fHgBFsXbOIA0unkKdkBUwtk/FLIwiCkA6keOVvyZIl9O3bl549e1K0aFHWrVuHoaEhW7Yk3RNoy5YthISE4ObmRtWqVbG3t6dmzZqUKlXqj4MXBCFj0NPTw9TU9LsPdSpVvjJ6+gYEBQbw4uljtc79O/oGBtjnzQ/A059Uj0wOiURC1mzKP8B9+hhErdp1Adi5M3mP/3pdhSrniZEF/PTDoYodtrZw/eZhEgj87ceL19ewtQU7Owlv3t9CJglKs4/oeB9evLrK5Wv7OHZiEwcPr8bt2HrOXdjJ/YenCfjkRSKBST62YhUvdHS0UvT90tHRZvTYCdx98JiWrdqQmJjI7BlTaehYm/fv3v30sTmsrTl17iLNW7YiPj6e/r27sXThPFR9BL9nn/5MmDIdgMljR3Dk0P5UjdO4WUvGTpoGwPTxw9NV25Qc1rmYv2wdALs2r+LmVfWs7vf5ZwwFi5YgOuwLB5ZMUvnPThAEIa2kaOUvPj6ee/fuMX78+G+3SaVSHB0d8fDwSPIxR48excHBAWdnZ44cOUK2bNno1KkTY8eO/aEf1VeaPB8kCIL6fPkcnOYFXwD09PQpX7k61y+d5dL5MxQuViLN50yJwsVK8Pb1Sx57PaRmHcdUj2OVw5rAgA8EBgTQsHFTKjlUYetWD8aO/Xm1T4CgINi6VULlKlWoVqPmT6+TyWQEfPAHoHTZcmRNxhLZquXKM1FODRpRvkKFlD2h35DL5Vy7eoVjR924dvUKTx57IZPJfvkYExMTihYrTtmy5XCoWo0aNWuTLVs2smXLRotWbVm9+gD9+yf+tNonQHQ0rFmjTcvWbb7teNmxey97XXczfIgzt27eoFqlsqzZsJmmzVsmOYaBgQEuu/YyecJYVi5bwsxpkwgKCmTOgiUqbXQ/cswEPgYFsWn9Gv7p35PsVjlwqFo9xeMMGzWeZ08ec/TwAZx7dcLt3LVvbUo0zbFBEzr37MeurRuYPnoge07ewNzCMk3n1NHVZerCtXRrXpsn19y5736UcvWap+mcgiAIqpCif2GCg4ORyWRY/c+7CCsrKwIDA5N8zJs3bzhw4AAymYyTJ08yefJkFi9ezKxZP9+aoenzQYIg/FpkZCSenp54enoC8PbtWzw9PfHxSVlJ+KsXTqdBdEmrUqseAJfc1TdnchUtrtwJ8fDBn/VUy5VL+Wbc79/S/KPHTSIsDBo2lBAUlPRjgoKU94eHw6ixE385/qePH5HJZEgkEqxy/L5qqkKh4NBB5WpT567dUvBMfi0mJoaVy5dSvHB+Gtavw5pVK3j00BOZTIaJiQlFihSlStVq1KpTlxo1a1G6TFly2dgglUqJiIjg1k0P1q5ZRbfOHbC3saJ6lYosnD+H9h06ExCgTbt2EqJ/0j4uOhratZMQEKDNyNH//4dQiURCh46d8bj9gIqVKhMWFkbn9m2YMHYUCQkJSY4llUqZPW8h8xYpE+QNa1cxsE+Pn16fGhKJhLkLl9KkWQvi4+Pp0bE1L71Tfr5UIpGwdPVGihYvwefgjwzu1SnVzeTTwrgpc8hXsDCfPwUxZ+JQtazEFShcnD7/KJvOH14+nfDPH9N8TkEQhD+V5n3+5HI52bNnZ8OGDZQrV4727dszceJE1q1b99PHjB8/nrCwsG8fvr6+aR2mIAgpcPfuXcqUKUOZMmUAGDFiBGXKlGHKlCkpGufS6aNpEV6SqtVxAuD+nZt8CfmstnmTo2TpcgB43v+z5M/WPg8A796+AZTNvxcvX42nJxQuLGH4cLh3D3x9lZ+HD4dChSR4esLiFWuo41j/l+OH/Pt9y2Jh8dOdG//10vsF796+QVdXl/pODf/ouX116sRxSpcozLgxI3n//h1mZmZ069GT7btcefH6PQHBodx9+JhzF69w4vQ5Tp27wPVbd/F+48Pn8GjuPPBi87YdDHQeTLHiyhXg+/fuMm3KJNq0bIqtXR7c3bUoWVKLJUuUZyHlcuXnJUugZEltLl7UY/fewxQv/uMKsn2ePJw9f5khw5RnXFctX0rzRk58+vjzxGDQ4CFsdtmJtrY2+/fupnuntsTGxqrk+wXKs3Hrt+ygfMVKhIWF0rlNc4KDP6V4HCMjI7buOoB5FgsePrjLjAkjfv8gNTEwNGTJmi1o6+hw6exxThzcrZZ5u/cfRuFipYiJCOPgkili+6cgCOleipK/rFmzoqWlRdD//Ak5KCiIHD/5K7C1tTUFCxb87o1CkSJFCAwMJP7rCfv/oenzQYIg/FqtWrVQKBQ/fGzbti1F43jeu0nwx6R3DaiadS478hcuhlwuT3erfyXLlEMikeDz/i2fPv5kiS4Z8vxb6v71f9pG9Ojdj/1uJyhctArLlkH58mBnp/y8bBkUKVaF/W4n6NGr72/H/1pB1DSZ/d6uXrkEQOUqVTE2Nk7Rc/lfiYmJjBoxlDatmuHn64uNrS0r16zjtc8H1m7YTOu27bCxtf1lMR9dXV2KFitGh06dWbR0BbfvP+TVe39WrV1P3Xr1kUqlvHj+jLi4RHx9pYwaBVZWoKWl/DxunBblKrTh4tVb1Kvv9NN5dHR0mDt/EXv2HcTExIRrVy9Tq2olvB49/Olj2rbvyO79h9DX1+f0yeN0bteS6J8tP6aCgYEBu/e5YZ8nLz7v39KzU5tUrdzlts/D2k3bkUgk7N25lQN7tqssxj9VrERpho2ZDMDimeP44Pc+zefU1tFh8oLVSLW0eXztnKj+KQhCupei5E9XV5dy5cpx/vz5b7fJ5XLOnz+Pg4NDko+pWrUqr169Qi6Xf7vN29sba2vrn/ZEEgTh73HuxCG1zVXTsZFyzlPH1DZncpiYmpG/YBEA7t6+mepx8hcoCChX3P6rjmN9Tp67zNWb95k5dyFjJkxm5tyFXL15n5PnLv92xe+ruH9Xo/T19ZN1/d1/2wA5/KYJ+u/Ex8fTuUNb1q5eCcA/w4bzwOsZvfr0w8DA4I/Gtra2pmfvvhw9cRrvt77MmD0X+zx5iI9PQKGANcBGlJ897jxkq8vuJFf8ktKseUsuXb1J/vwF8PX1oX7t6pw68fPfvQYNG3PA7ThGRkZcPH+Ozm1bqDQBzJotG64Hj2JqZsadWx6MHDIgVStVtR3rM2biVACmjhvGsyePVBbjn+rrPJxyFR2IioxgxphB3733SCsFChenl/NIAA4vn0ZU2Jc0n1MQBCG1Urztc8SIEWzcuBEXFxeePXvGwIEDiYqKomfPngB069btu4IwAwcOJCQkhKFDh+Lt7c2JEyeYM2cOzs4pLzktCELmc+boAbXNVat+EwCuXHQnRoVvqlWhfCXlH9Bu3riW6jEKFSkKKLd9JpU0FCtREuchwxk3cSrOQ4ZTrETJFI3/9Y10cguSPH2irKxaqnSZFM3zXwqFgv59e3H82BH09fXZs+8g8xYsxvBXFVlSydrampGjx/LoqTfrN28FoCnQ59/PmzasIywsLEVjFi5ShEvXblK7jiNRUVF0bNuKDevW/PT6GrVqc+joSYyNjbl86QKd27UkJiYm9U/qfxQsVJhtO/eipaXFAdddrFmxJFXjDB05jrr1GxIXG8s/fboQEZE+CrNpaWmxYOVGDAyNuH/rOvtc1qtl3p4DR5K3QBEiQ0M4sirt200IgiCkVoqTv/bt27No0SKmTJlC6dKl8fT05PTp09+KwPj4+BAQEPDteltbW86cOcOdO3coWbIkQ4YMYejQoYwbN051z0IQhAxJIpXy9NF93r95+fuLVaBg0ZLktM1NbEw0ly+cVcucyVXRQVmB0eMPmn5ny25F1mzZUSgUPEuDlhZft+8nJiYm6/o3r18BUKBgoVTPuWbVCva57kZbWxvXA4dp1iLp6plfyWQyrl+7yqzpU2nTohllSxTFNkdWLE0NyWZuTB5bayqVK0371i2ZOmkCR90O8/F/zuNpaWnh1KDRD2OvW7OKUsUL4bJtS4pWlLJkycLhoyfo2asPcrmcUcP+YdqkCT9ddXOoWo1DR09iZGTE5Yvn6dG5nUqLq9Sq48icBcqkb9bUCVxwP5PiMaRSKSvXbyGXjS3v3rxi0sjB6ea8W277vIybOhuA1Ytm4PP2dZrPqaOry6R5K5FIJNw768aLO1fTfE5BEITUSFXBl8GDB/P+/Xvi4uK4desWlSpV+nbfpUuXfjj34+DgwM2bN4mNjeX169dMmDAhWcUCBEHI3AqUVW4HPOW2Vy3zSSQS6jg1A+D0scNqmTO5KlapBoDXI09Cv6R+21iJkqUBeOT5QBVhfUf/3y2WsclYiYqIiPi2SmZnlztV871984Ypk5Q7SeYtXPzLc3ZhYWHMmz2TQvlyU79OTebOnsmpk8d58eI5ISEhxMbGEh0dzcegIB57PeL4sSMsWjCPju1ak8cmB5XLl2HG1Mk89vp5r8W8efPx6eNHBvXvQ/26NXn+7Fmyn4uOjg4r16xn6vSZACxZNJ8hg/r/tDVF5SpVOeB2HAMDA86dOUW/Xl1/28YiJfr0H0TXHr1RKBQM7NWVd29SniBZWFiyfusutLS0OHHkAHt3blVZfH+qU/e+VK1Rh7jYGGaOdVbp9+5nipcuT/vu/QE4sGgScTHpa3eBIAgCqKHapyAIws+UrqvchnnysKtazuYAODZWrhy5nzlBdFSUWuZMDqscOclXsDAKhYLrVy+lepyS/26xvHf3jmoC+w+Tf3syhof/fuvj5+BgQFloJLXFXqZOnkBsbCy16tRlwKDBP71u757dlCxSgJnTpxLw4QPm5ua0a9+RxctWcuK0O/c8n/D85TuevniDx+0HHD56ksVLV9CjV59v5/e8Hj1k/tzZVCpXisrly7B925Yf5jl9/hKz5y3AyMgIjxvXcahYhoUL5iZ7JVQikTBm3ETWrNuIVCrFZetmenfv/NPWDlWr12D3vkPo6upyzO0Qw/8ZqLLVNYlEwoIlK75VAO3VtV2qzheWr1iZ8VOUCe2syaN5+SL5CXFakkgkzFmyBkMjYx7eu8n+7RvUMu+AEZPIkdOGkEA/zm5boZY5BUEQUkIkf4IgaEzRyrXRNzIm8IMf92+l/qxbShQpUebb1s+L506pZc7kqlajDgCXzp9L9RjlKih3Yty9c0slMf2Xxb+Ns0NDQ3+b8HytDGqSymrNL729OXhgHwDzFixOsopnYmIiQwcPpFf3LgQHB1OoUGG2uuzirW8g23bsZuCgwdSuU5ciRYtilzs39nnyUKp0aZwaNGSg8z+sWbeR2/cf8d7/I5u2bKdJ0+bo6uri9eghUyaO/2E+XV1dho0Yxf1HT3Fq2Ij4+HimTZ6Ik2Mt3r19m+zn1r1nb3bu2YeOjg6HDuynW6d2P61+Xbdefbbu2I1UKmWnyxZmTZuU7Hl+R09Pj2279pEtW3aePvZi7IjUbd0cNGQEterUIzYmhuEDenwrDKRpuWztvm3/XLN4Jv4+79J8TkMjY0ZPXwTAlf1b+PAqfSTDgiAIX4nkTxAEjdHR06N0HeXq37EDu9Qyp0QioX6T1so5D+9Ty5zJVb22IwAXzp9N9QpPuYqVAfB+/owvISEqiw3AwtLy25b9oMBft+j4msyktqrztq2bAGjQqDElSv5YmEYul9O/Ty82bViPRCJh4uRp3L7/iPYdO6Gnp5eiubJly0anLl3Zd9CNNz4BLFqynLx58/1wXVhoKAA2trYcdDvG+k1bMTU15abHDRwqluHwoeQXL2reohV7D7ihp6fHiWNHf5kANm3ekhWrlb1xly6az+YNa1P0/H4lZ85cbN6+Gy0tLfbv2ckulx9XPH9HKpWyYt1mLCyz8fypFwtnp6zfZ1rq0LU3larUIDYmWm3N36vXaUCdhs2Ry2QcWDxZbbsaBEEQkkMkf4IgaFTFhm0AcD91hMiIlFVSTC2npso5L50/Q+gX1SZIf6JSlRro6evj7+vD81QWbLG0zPqtwIrHH1QOTYqWlhY5c9kA4Ofnq9Kx/0uhUHxb9eveo1eS1yxeMA/X3crG6LtcDzBx8lR0dHT+eG4LCwsGDR7C+cvXf7ivZtXKrF+7GplMhkQioUu37ty860llhyqEh4fTpWM7xowa/tNtnP/LqUFD9h86ir6+PiePH6NXt04/XVHt1rM3E6dMB2DsyKGcOXU89U/yf1SrUYuJU2YAMHHMMJ54/bwf4c9kt8rB8rUbAdi2YRXXLp//zSPUQyqVMnvJavT09Llz4zLHD6rnj0wjJs1Fz9CY908fcOu4q1rmFARBSA6R/AmCoFF2RUtjZV+AhLhYzhw7qJY58xUqSoEixUlMSODkUfXMmRwGhoZUqVYLgDMnU//m3qFqDQCuXr6kgqi+l9veHoC3vykQ8rUXYGwqtgC+9PbG18cHPT09HJMo8uL16BEzpyv7zC1ftZYWLVuleI7fSaqdRWjoF0YM/YeaVSvj+UBZUCe3vT2n3S8yfORoAFavXE6zJg34/Plzsuap61gP1/2H0dXV5ajbYQb27fXTlaIx4yfSvWdv5HI5fbp3xuuhZ+qeXBKGjBhNPaeGxMXF0b9nZ6IiI1M8Rj2nRnTvrSx4MnZof8JC00e/O/s8+Rg2Vtn8ffmcSYQEf0rzObPnyInziIkAnNiwiMjQ5P0+CIIgpDWR/AmCoFESiYRKjdoCcMTVRW3zNmrRHoDD+3arbc7kqNtAuQ329MnUN6KvVrM2AJcuuqskpv/Kl1/ZSN77xYtfXmdsbAJAeFhYirfa3brlAUD5ChWT7Oc3acJYZDIZzVu0okfP3ika+0/MmD0Xc3NzHty/R40qFZk5bQoJCQno6Ogwa+589uw7iLGxMVcuXaRWtcq89PZO1rj16juxa89+tLW12btnF2NHDU/yeyaRSFiyYjW169QlKiqKTu1a/nb7bXJJpVLWbNiKdc5cvHrpzcSxw1M1ztRZ88mXvwBBAR+YPn6ESmJThZ79/6FI8ZKEh4WydPYEtczZpmtfChYtQUxEGMfXLVDLnIIgCL8jkj9BEDSunFNLtHR0ef7kIc+8PNUyp1PzdmhpafHg7i1ev/x1IqNOjk6NkUgkeN6/i5+vT6rGqF6zDlKplBfPnuLv76fS+AoVLgLA0yc/b4kAYJk1K6A8+xcREZGiOZ49fQJAydKlf7jvsZcX7mfPoKWlxZx5C5MsBJMUmUzG7Vs3Wbl8KcOHDqZnt8707NaZYUOcWbxwPieOH/uh39//6t6jN/cfPaNV67bIZDLmzZlF3ZrVePNauQrarEVLLly5QW57e968eU2dmlW4ddMjWfE1atKUDZu3AbB+zSoWL5iX5HU6Ojq47N5HgYKF8PfzpXvntirrAWiZNSsbtmxHIpHgutOFI4f2p3gMQ0NDVq7filQq5eihvZw54aaS2P6UtrY2cxavRiqVcubofm5evaCWOcdMXwzAnVMHePf4fprPKQiC8Dsi+RMEQeOMzS0oWUO5ve/wHvX0CsuazYrKNZQFVg667lTLnMmRNbsV5Ssp+x+eOJq6XoRZLCwoU64CAO5nT6ssNoASJUsB8MjT85fXGRkZYfpvpc8P/v4pmuP9u3cASRZd2b1rOwBNmjYnT968vx0rIiKCubNnkj+PDbWqOzB29AjWr13NXtfd7HXdzYZ1a5g8cRxtWzXD3saKCmVKMH3qZF6+THrVLkeOHOzcs4/tO10xNzfn3t07VK1UjmNH3AAoVrw4l67dpHyFioSEhNC4gSNnzyTvZ9C+QycWLl4GwIypk3DdnfTvpbm5OXsPHcHM3JzbNz0YN2pYssZPjqrVazJijLLS6Zhhzvin4mxn2fIVGTxsFACTRw8l5HOwyuL7EyVKl6NrrwEALJgykri4tK9KWrJsRZq27QLAoWXTkKuh36AgCMKviORPEIR0waFZRwBOHt2vtsIvzdp2BuDwvp3J7tWmDg2bKs+wHT2c/OqR/8vRqSHwZ2cHk1KiVBkkEgl+fr58DAr65bV2ue0BePf2TYrmCP73TJaVVY4f7jt94gQA7dp3/O04Nz1uUK50MWZOn0JQYCDm5uY0adac0WPHM2/BYuYtWMzY8RNp36ETRYoWRSKR8OTJY+bPnYVjrWq/HLtNu/bcvvfoW7GXDm1bMWv6VORyOdmzZ+fk2fPUb9CQmJgY2rVuztEjyUvkBw0ewtDhIwFw7t+HG9euJnld/vwF2OyyE4lEgsuWjex0Ud0fTcaMn0zZ8hUICwtl2KC+qapWOXLcZAoVKUrI50/MnDhKZbH9qWHjpmCVwxo/n7e4rFuqljkHj56GvrEJ/i+fcPP4XrXMKQiC8DMi+RMEIV3IW6oiVrnzEx8TzcnD6nmDVK12Aywss/HpYxAXz55Uy5zJ0bBZS6RSKffu3OJ9ChOnr5waKs8OXrrgTpQKm9mbmppSqHBRAO7cvvnLa/Plzw/w01W0n/nabNzIyOi720NCQnjx4jkANWvX+eUY7ufO0rB+Hfx8fbHPk4et23fx3j+I/QfdmDFrDkOHj2Do8BFMmzGLbTt2cf/hE3w+fGTLth00btL0W0uL//rfc3g2traccb+E8z9DAZg7eybdO3ckJiYGIyMj9h44TJu27UlISKBLx3bJbgUxa858WrZqQ0JCAp3at/5pD8H6Tg2/VQAdM+IflRWA0dHRYd0mFwwMDLh6+QJbNqa8tYSenh7LVm9CKpVy7PA+zp85oZLY/pSJiSkTZijP321ftwy/98nvz5haWSyz4jxcWfzl1KbFRIeHpvmcgiAIPyOSP0EQ0gWJREKVFsqVuIO7NqulH5eOri6NW3cCwHVnyvubpZVs2XNQuWpNAA4fSF0iXKRYCXLb5yU2NlblWz8rOSi3pV67euWX1xUuUgyAJ785H/i/vv3s/+c834vnyobZtnZ2WFhY/PTxb9+8oXOHNsTFxdGkaTPu3H9Eh46d0NXVxcfHh3lzZtHIyZF89jZYmhmR3cKUooXy0btHV7y9XzB0+Eiu37z7w7htWzXjsdf3z0VHR4eFi5exftNWZdP2g/tp1siJL1++oKury5btO+nYuSsymYweXTtx4tjR3z5/qVTKhs3bKFO2HCGfP9OxbUsif1J9c9TY8dRv0JDY2Fh6detIeHj4b8dPjvwFCjJ99nwAZk+dwJvXL1M8Rply5RkweBgAU8YOJSJCNbH9qUbNWlG1Zl3i4+NYPGOsWv5f07pLH/IVLEp0eCintyxL8/kEQRB+RiR/gqBhbm5uSCQS1qxZ893ta9euRSKRYP9vaf2vIiIiMDMzo3bt2mqMUj3KO7VEz8CIt69ecOfGrxMLVWnRvjsAVy6cw8/nvVrmTI7mbToAcGDvrlS9OZVIJDRu1gKAI3+wfTQp1WrUAn7fSqJkKeX5wK9tEZLrW5uImJjvbvf3Uxavyf3vdtKfGTliCBEREThUqcou1/0YGxsTHR3NiGFDKFowL9OnTubihfN88PcnOjqaiIgI3r55w9kzp5k3Zxb169aiScN6P4x75/YtqlQqy4x/q3z+V9duPTh28ixmZmbcuH6NBo61+fjxI1paWqzftIX2HTuTmJhI187tuXTx98VGDA0N2XfADascOXjy2IvBA/ok+XsglUpZv9kFGxtbXr96yZjh//x27OTq1XcANWvVISYmhuHO/VK1/XPU+CnY58lHUMAHlsyZprLY/oREImHqnMVo6+hw/dJZrl1Q7R9HkqKtrc3wSXMB8Di6m8C3KVsNFwRBUBWR/AmChmXJkgXgu4qIcrmcpUuV51G+fPm+V5aLiwvh4eGMGJF+yqirir6RCeWcWgKwb/s6tcxpa5+XilVroVAo2LN9s1rmTA6nJi0wMDDk1Utv7t+9naoxmrVUttA4c/L4T1eOUqPGv60kHj30/OW5v3LlKwLw9MnjFM1vbq58TYSEfN8bLTw87Lv7k/LQ05PTJ08ok66NW9DV1SU0NJR6dWqydvVKZDIZtWrXYeXqdVy+dpOnL17z6MkLzl24zPKVa+jQsTMWFhYEB/9YpKRBw0YkJiYyb85Mateo8q3K51c1atbi7PkrZLey4rHXIxo61iYoKAgtLS02bN5K02YtiIuLo0PbljxMxhbNnLlyfWsBcejAftauXpnkdZaWlmzZvgupVMo+113sd1VN+xKpVMryNRswNDLilsd1tm5K+WvS0NCQhctWA7Bz63oe3r+jktj+VN78BenVX5koL501gXgVVUz9lYpVa1KrfhPkMhlHVs9Ry4qjIAjC/xLJnyBoWFLJ37Fjx3j58iXNmjUjIiIC2b8V4hQKBf/H3l1HRbl1ARz+TdCNgiJSdndhYIud2IpiY2Jjd3djd3f3tbuwO7BBEEnp+f4Y5LteRWpmQD3PWrPuusP7nrMHRGfPOWfvhQsXkjt3burXr58u8apbxaauAJw7eYR3r19pZM5mbZW94rZtWkNkKpqSq4OhoRHO9RsDsHn9mlSNUbR4CXLkzMXXr185uG+PymKzsLSkaLESABw7kvhZyWzW1tjY2BIbG5vslgcAVlZWwP9X+r75VpTnZ+fxvtkWn/g0atKU3HnyoFAo6NCuNTdvXCdTpkzsP3SUw8dO0qVbd8qULYtDjhzkzpOHipWc6NbDndXrNvDq7UdWrf2x0qaNrS3LV63FzMyMmzeuU6FcSQ4f+v4sW+EiRTjxzzmss2fn0aOH1HOugb+/P3K5nDUbNuFUuQohISE0a1z/h9f3M47lKzBl2kwARg0bwo3rP0+eypWvgOeI0QAM6t+bNypaxba1s2fsBOWK1eRxI1NV/bNSlWq4tGqLQqFg1JC+CX+fpbee/YcmFH/ZvHpx0jeoQF/PCci0tHly7RyPrpzWyJyCIAj/JpI/QUhnpqamwPfJ36xZsyhZsiQNGjRAoVDw5csXAI4dO8bjx4/x8PBIdn+z300Wu5zkLVMJhULB1nVLNTJnpep1sMxqTWCAP4f27dTInMnh0lqZCO/esZWwVKzcSSQSmrZQVsXculm17Sxq1akLwKGDv25GX6GSEwBnTie/r5p9fAuH5/9ZWdOJ3w76NeLrD/d8czp+noaNlCvIu3bu4NjRI+jp6XHwyAlq1Kz1wz1RUVG8eP6cRw8f4ufnh1wu/+l1y5d6MWHcaBYsXko5x/IEBQXh0qQB8+fO/m4VJ1fu3Bw9fpps1tY8fHCfJg3qEhoaiq6uLpu37yJ/gYJ8eP8el6YNk1WMx71XHxo3aUZ0dDRu7RI/1zdo6DDKlitPSHAwvbp3StU2zZ/p1LUHZR3LExYayrBBfVO1YjVm4jSMTUx5cPc2G9csU0lcaWVoaMSgkRMAWLVoJv5+H9U+Z3Y7B1p36A7A/sVTic1AVYYFQfg7iORPENLZf1f+rl27xrlz5xgwYAAmJibA/7d+zp8/HzMzMzp0UJ5T27VrFzVr1sTc3ByJRMKr+P5ovzun5p0A2L11vUbaPsjlcpq1Vc65dsXiDLMdq2z5StjnyEVYWCh7dm5L1RjNWyqL6Jw5dZK3qVi1SUy9+o0AOHn82C8TmKrVlb0Ujx87muyx88dXE31w/953z2cyzwRAwE+2ZIJyu/S3e0qXVm45nTdH2WS7/8DBFP1P0/izZ07TtFF9LM2NKZgvF8WLFMDOOgu22Szp3rXTD+Pb2Njy2seH9m1aUqVqNTp36YZCocBzyECGDR30XbKVI2dODhw6TubMmbl54zptWzUnOjoaU1NTdu7Zj4WlJXdue9Oz+8/P8v2bRCJhkddy7OzsefXqJQP79f7pdXK5HK+Vq9HX1+f82TOsWKqa1SypVMqcBV5oaWlx7PBBDh/Ym+IxLCwsGT5amWjNmTqegE9+KoktrRo1a0XREqX5Gh7GklkTNDKnW6+BmJiZ4+vzjCui9YMgCBomkj9BSGdGRkbI5fKE5G/WrFnY2NjQokWLhOTv8+fPPHv2jMOHD9O9e/eEEvhhYWE4OTkxfvz4dItfHfKWrkQW+9xEhoeyd+s6jczZpFVHtLV1uHf7Fjev/bqFgaZIJBJatY9PSlelbrXEziEHjhWdlGcaN6xVWWyFixbD3iEHX79+5cgvegnWqOmMRCLhzm3vZG1zBCharDgAjx4+SGj7AGBtYwOQ6JbGL1++EBl/diu7jQ2+vr5cu3oFiURC1+7uCdcpFArGjBqBc42qHD50kMjISPT09DAzM0MikeDv78/hgz++pqMnT9OhYycUCgVTJ0/kw4f3jBk3EYD5c2fTp1eP7xLAfPnzs3PvQfT19Tlx7CiD+itXzezs7dm0dQdyuZwd27eyYF7S/eZMTU1ZtXYDUqmUrZs3smvHzz8MyJkzFxOmKFsZjB89PMU9FhOTL38B+vZX9usbOXRAqlai27t1oUjR4oQEBzFj4iiVxJVWUqmUkRNmAHBg5yYe37+t9jmNjE3p2tcTgKNr5hERrrrzuIIgCEkRyZ8gZACmpqaEhITg4+PDjh076NOnD3K5/LuVv4ULFyKXy+nd+/+f+rdv355Ro0ZRpUqVdIpcPSQSCU7N3QDYsmYpMf+prKgOpuaZqN24BQCrlv68sEZ6aNqyHdo6Otzxvpnqwi9t2ncEYP2aVSo7byWRSGjqovx+bd+6OdHrLCwtKVPWEYAD+5O3YpTN2pps1tbExsZy7eqVhOdz5coNgJ+fH58/f/7hvm+Jn1QqRVtbm9veyiqjefPlI2vW/zeMX7FsKdOnTgagc5du3PC+R0BQGO/9PhMQFMapsxfp6/FjQaUTx46yZNkKVq5eh46ODocOHmD/3t3MmjMfqVTK6pXL6d+v93creaVLl2H1uk1IJBJWLFvKimXKoinlK1Rk2szZAIwa4ZmsM5HlHMszeOgwAAb0651osZ3OXbtTyakK4eHh9O/jrrKV7AFDhmNn78D7d2+ZM2Nyiu+XyWRMnjkPgB1b1nPn1o/tNNJD8VJlqN+4OQqFgrmTR2pk5b9pazds7HMSGhjAqc0ZYxusIAh/B5H8CUIG8C35mzdvHnp6enTr1g0gIfl78+YNq1evpkWLFlhbW6dnqBpTsmZjjMwz4/vhLScO7dbInK07KleHjh/ax+tX6m/+nBzmmTJTr5ELACuXLkrVGPUbNcPU1Iy3b15z8rjqytq7tFT2SDx25DD+nz4lel3DxsrzdzsTWa36L4lEQqX4dhKnTp5IeN7IyAiH+POAt27e+OE+PT09QLn9MzIykg/v3wPft4YICwtjzKjhAEycMo2FS5ZSoGDBhDO0enp6lHN0ZNAQzx/G79vbnbatW1CvQUOOnTyj3NJ58wYrlnsxe+4CJBIJy5cuYcK4Md/d16BhI8ZPVBZNGTzAg6tXlCvL3d174dK8JTExMbi5tiUoKOktzp7DR1GkaDE+BwQwKJG2DlKplPlLlqKrq8uZUydVVv1TT0+PKTOUCevSRfN4/izl7QpKlSmHSyvlVuSJo4ZkmC3Wg0aMR1tbhxuXz3Hh9DG1zyfX0qL3EOWfk7PbVhEckDG2wQqC8OcTyZ8gZABmZma8e/eOFStW0KlTp4Sk79t/58+fT3BwMP3790/PMDVKS0cnofLnumXzNPImMWfeApSrVJ24uDjWLFuo9vmSy7VzDwD27d6B78cPKb5fT0+Plm2V38uVy1TXQiNf/gIUL1GKmJgYtmzemOh1TZopW05cOH+ON69fJ2vs6jWUffaOHjn83fPfVhF/1mDexMQEHR0dAN6/e0dUVBQA2vHPARw7eoTAwEDs7O3x6D8wWbF8I5fL2b1zB5XKl8Hc3JyTp8/HF3V5wIplXkydrjxfOHXyBDas+36L7YBBQ2jS1IXo6Ghc27YiMDAQiUTCgiVLsXdwwMfnFYMG9EsyBm1tbbyWr0Imk7Fn104OJrKamjNnLoYMGwnASM9BfPlPy5jUcq5Tnxq1ahMdHc2Y4UNSNcaIMRPR09Pn5rXLHNqbMQosZbe1o0PXngAsnDZWIxVJq9RqQKHipYmK+MqxNRlnt4EgCH82kfwJQgZgZmaGj48PYWFh9Ov3/zeA35K/u3fv4uTkRMmSJdMrxHRRvnE7tPX0efboPpfOnEj6BhVo11W5mrJt01oC/9NnLr0ULlaSkmUciY6OZvXyJakao2Pn7kgkEo4fPczzZ09VFlu7DsrtuWtWLk80Qc9uY5OwkrdpY/LOcNZyroNUKuXObW9evfz/Kmzlqsoeg/+cPP7DPRKJhJw5cwHw8OEDDI2MAAj+14rat1YJzs51ftky4ptzwK74/27auoPsNjY8ffKEqk7lCQ8P59iJ02S1suLevbvs27ubQYOHAtC7Zzeu/mvLqkQiYcmyleTImZM3r1/Tr5dyldnY2JgVq9chlUrZtGEdB/fvSzKmokWL4TFAef5ukEffRHso9u0/kLz58uPv/4kpE8cmOW5ySCQSJk2bhVwu58TRQ5z+yc8hKVbZrOkdf35wxsRRCdt101uPvoMwNjHlxdOHHNylmtXSX5FIJPQeMhaAKwe38ultxthtIAjCn00kf4KQAXyr+Nm4cWNyxG9rA2WDZLlcDvBXrfp9o29kgmMDZauCNV6zNTJn6fKVyVuwCBFfw9mwWjOtJpLDLb4h9dqVy5LVHuC/HHLmonqtOgAsXay6VYZmLVpjYGDAk8ePOH/2TKLXtXVVVqhdt2Z1sloQWFhYJCSM27dtSXi+Vq3aAFy/dpUPH35cBS1WvETC121sbQF48eL/LSO+VQq1zp490bl9fHwYPWIYcsAV6Br/387tWlOjek0KFiyEv78/dZ2rExERwf6DRzE2NubC+XP4+/vTsHEToqKiaN+mRUKlXlAmemvWb0Ymk7FzxzZ2bFNWenQsX4F+8auQ/fr2TNb2z2EjRuPgkIN3794ybfLPq1Rqa2szc858AFYuW8KDe3eTHDc5cufJS5fuylWysSOHpGqVrEfv/mS1ysbbNz4Z5vfMxNSMnh7K1cxlc6cSGan+np8lylSgQpVaxMXGcmTlXLXPJwiCIJI/QcgAtmzZgkKhYOfOH7dARUdHo1AoaNy4seYDywAqt+iETK6F97VLeF9PfqPw1JJIJLh28wBg3YolhKci0VKHmnUaYGPnQGDgZ7ZsTF3Vzm7uygRy4/o1BP6kYEpqGBsb06J1OwC8fpFUNm7qgqmpKa9eveTY0eSdO2zZSpn4b96wPmFV0SpbNsqULYdCofhpxctvfQX/OXmCQoUKA/Dm9Ws+xZ9J/NYrMLEE+trVq1QoUYQ7G9axCggBAuL/u+jrV+5u2sCH1z7kL1CQwMBAGtavjZm5ORs2b0MqlbJm9UqqV69Jzly5ePP6NX16dv9uRbRUqdIMjd+OOdCjD/7xyeiI0WPJlSs3H96/Z9zoEUl+b/T09Jg5W1k8ZdH8uTx98vin11WuWo1GTZoSFxfHCM9BKts+PWTYKExNzXj04D5bk7ma+28GBgYMGa4887Z4zjSCg76oJK60at+pB1mzWeP38R07NqzQyJzug5SVT73/OcD7Zw81MqcgCH8vkfwJwm/s8+fPeHt78/ix8o3fgwcP8Pb2/mklRFVbtGgR9vb26OrqUrZsWa5eTV0lyqSYWGSllLOyYMjqRbPUMsd/VavTiOy2DgR+DmDL+lUamTMpMpmMzu59AfBaMJfoVFRArVSlGgULF+FreDirVqju7F/XHr0AOLh/Hy9f/Ly1gL6+Pm1dOwLgtTh55ymbNGuOvr4+jx8/4uKF8wnPt4hPCjes/zEJruWsXN28euUy4eHhCQngyRPK7Yn2Dg4APPlJsuTj40OTOjVpEBrKleho2gO68V/TBdoDl6OiaBgWhu+b1+TMlYv3797RpqULlatUZdSYcQAM9xzM5CkzkMvl7Nq5nd07d3w3zxDP4Qmrh6OGK7eJ6unpMXehsi/f8mVe3L7tneT3p3bdejjXrktMTAwjPAcnet2EydPR1tbmzKmTnDh6ONHrUsLUzIyBQ5WFc2ZMGf9dS47katnWlTz58hP0JZBlCzWzsp8UHV1d+g5SJt9rveYQFhqi9jnz5C9MrfrNADi8Mum2H4IgCGkhkj9B+I3t27eP4sWL4+KirAZZr149ihcvzr59SZ8bSoutW7cyYMAAxowZw82bNylatCjOzs74+amnYl21tj2QymRcOnuCB3duqWWOf5PJZLj2UG6zXbF4DpER6t/+lRwurVwxz2TBm9ev2LMz5c2hJRIJvfoptxcuXbQgVW/YfyZf/gJUq1GLuLg4Fs5P/M1r1+49lecOjx3hwYP7SY5rbGyckOh5Lfp/wtiiVZuEVg7Xrn3/oYO1tTXlHMujUCjYsnkjderVB2DXzu0AlIpv/n7+7JkftivOmz0T+69fWR4XhzyRmOTA8rg4HCIjcSzniKmpKVevXGbyxPEMHjqMipWcCAsLY8niBQkVQwf07/PdVk5tbW0WLFZudVy3ZjXX419D1WrVcWnekri4OIYO6p+sVbqp05Xn744cOsi5M6d/eo29gwM9eilXfceOGq6yYiZduvcku40tH96/S9VZVJlMltD4fe3yxXzy+6iSuNKqact2OOTMzZfPAWxZo7oPSX6lq8cwJFIpDy6exOeBt0bmFATh7ySSP0H4jXXs2BGFQvHDo2PHjmqdd/bs2XTt2hU3NzcKFCiAl5cX+vr6rFqlnlWyzNZ2FK/WAIBVi6arZY7/qtekFZZZrfHz/ciOLZppNJ8UXT093Lor+zzOnzUtVW/iGzZpjq2dA/7+n1i/ZqXKYuvjoUwq169ZxadEPgTIkTMnDRo1BmDu7JnJGrdHT2XSsnfProTCL5kyZaJZ85YALF4w74d72sWvMK5cvpTmLVoBcPjgAT5+/EjZsuUwNTXF39+fc/86oxgaGsrGNavoFx2daOL3jRzoGxXFvl07mTVXudV15vSpPHzwgGUrVqOnp8fpU/+QK3cecufJg5+vL1P/cy6vnGN52rZTVmAdNuT/2zEnTpmGrq4u586e4cihg0l+f/LkzUunzl0BGD1yWKIJ48AhwzAxNeXhg3vs/NcZyrTQ0dHBc4Ry6+bCOTMICQ5O8RjOdRtQvGRpvn4NZ+l8zazsJ0Uulyes/m1auZCQ4C9qn9POIRf1mij/rB5ZNVft8wmC8PcSyZ8gCCkSFRXFjRs3qFGjRsJzUqmUGjVqcOnSz8/kRUZGEhwc/N0jpaq3V64anT1xmCcP7qQ6/uTS0tbGtbuy8qrX/JkZpiJhu07dMTYx5emTxxzYuyvF98vlcnp7KCstzp89gwgVrWo6ValGiZKliIiI+OXqn8dAZUGNLZs2fFfFMzGFCxeheo1axMbGMmfW/xP/Xn2VP5sd27f+sNW0Zas2mJmZ8eL5c54/f0bZco7ExMTgtXghWlpauMQnjkv+tf306pXLhH/9SvNkvt4WQPjXr2TNmpVGTZoSGxvLkEH9cciRI6ER+4Rxo5k8dYZyrkULfmhzMXbCZPT09Lh44TxHDx8CwMbWFvdvq3RjRiarOI7niNHo6+tz49pVjhw68NNrzMzM8Big3Bo6bfL4VG0b/pkWrduSO09eAgM/s9wr5YWEJBIJniOV22U3rVvBxw/vVBJXWtVr7ELuvAUICQ5i8+rUVdhNqc69hyCVyXly7Rwv7/3Yx1IQBEEVRPInCEKK+Pv7ExsbS5YsWb57PkuWLHz8+PNtW1OmTMHExCThYWNjk+J5s9jlpFg15Ra+5fOnpTzwVGjU0pXMlln58O4tOzPI6p+RkTEduynP2M2ePilZycF/tWzrSjbr7Hz48F5lq38SiYRBnsrVkmVLFiXa9L1U6TJUrV6D2NhYZkyfnKyxvyVT69as5u2bNwAUL16CGrWciY2NZeqUid9db2BgQNf4apSTJ4yjr8cAQJmABQQE0LO38uzkvj27uXP7NgDBwcEYy+UJZ/ySogsYyeUEBwczbfostLS0OPXPSS5euEC//gPJamWFz6tX+H78SOUqVYmKimLG9CnfjWFtbY17/MrmpAnjElbtBgweirGxMffu3mHf3t1JxpIlSxZ69FSuCE+ZOD7R1b8evfqQ2cKCly+eq6zxu1wuZ8gwZcGSpQvnfddWI7mcqlanrGMFoiIjWbYgY5z9k0ql9B2s/PO8edUSjRSksba1p34z5TbnY6vnq30+QRD+TiL5EwRB7YYNG0ZQUFDC4038G/iUqunaG4lEwpnjB3l0z1u1Qf6Ejo4uHeLP/i2eOz3DrP517NoLYxNTHj98wN5dP1a8TIqOjg59+itX4ObOnMbXr19VEpdznfoUK16SsLCw71bp/mv4SOVWwfVr1/DsadI9Bys5VcapchWioqKYNGFswvMjRinH2bh+LY8efl8lsU+//hgbG3P37h3Cw8MoUqQowcHBTJowjvwFCuDSQrn6N7B/XxQKBcbGxgTHxJDcddAIICQmBmNjY+zs7WnXXtnKYtHCeejr69M/fpVt/rzZDB85Ov71rk6oOvpNvwGD0NPT4+aN65z65yQA5ubmCat/M6dPTdbZv379B6Gvr4/3rZscP/bzaqoGBgb0jd+eO2fmVJWd/WvcrLmycEvQl1Sd/ZNIJAwcqqyAumXDKvx8f2zhkR6c6zUiT76ChIUGs3WtZs7+ufUcqFz9u36eV/duamROQRD+LiL5EwQhRTJnzoxMJsPX1/e75319fcmaNetP79HR0cHY2Pi7R2pksc9FserKs3/L5k1J4mrVaNyqA5ZZs/Hx/Tu2ZpDKn8YmpnTqoUwOZkweT0xMTIrHaOPqRnZbOz58eM/KZarZ1iaRSBg2aiwAy70WJ6zS/VdZx/LUql2H2NhYxo8dlayxx01QrhJuWLeWe3eV/erKlC1H/QaNiIuLY5jnoO+uz5QpE4OGKFcMRw33ZGR8Jc6lSxZx6+ZNJk6ehp6eHufPnWWZ1xLKlC2Hvp4e25P5WrcB+np6lC3nCEB39/9XPA0JCcGtcxcMDQ158vgxEomEEiVKEhkZybo13/8ZsrCwoGOnLgAs+tf5xZ59+qGnp8etmze+O5uYmMyZM9O5a3cA5s6ckeh1Xbq7Y2ZuzvNnT9mfjFXF5JDJZAwYpCxus3Tx/FT1oaxUpRqlypQjKjKSlUsyxqqXVCql1wDl69qyegmhISnfrp5S1jb21GuqPPt3fF3yquIKgiCkhEj+BEFIEW1tbUqWLMnJkycTnouLi+PkyZM4OjqqfX7njn2RSKWc/+co97yvq30+HR1dOvZUrpYsnjstw/T969itN2aZMvPi+TO2bVqf4vt1dHQSVlvmzJiaqu16P1OjVm3KV6xEREQEk/+1SvdfYydMRiKRsHPHNq5euZzkuGXKlqNJUxfi4uIY8q9KmBOnTENLS4ujhw9x8MD+7+7p068/uXLl5uPHjxw/eoRmzVsQFxdHt84dyZo1KxMmTQVg6OABPH3yhLYdOzFPS4ukUukYYL62Nu3cOmNgYABAkaJFyZEzJ5GRkZw7ewYjIyOaubQAYMe2rXTt7g4oVyn/u5L3bevn0cOH8Hn1ClAmc23bKwvCJLc1Rp++/ZHL5Zw/d4ZbN39+ZszQ0JDu7sotogvmzFRZ37+mzVti75CDzwH+bN6wJsX3SyQSPAYrk/XNa1fwJVD97WqSo06DJuTMnZeQ4CB2blRdgaRfcXMfiEQq5dGVM7x5fFcjcwqC8PcQyZ8gCCk2YMAAli9fztq1a3n48CHu7u6EhYXh5uam9rktbBwo5dwUAK/ZE5O4WjUaNW+PVXZb/D/5sX6VZrZ/JcXQ0IgefZWrXTOnTkjV1s3mrdqSO28+AgM/M3eWas5RSiQSxk5UJlUb16/lTiL96goVLkLb+K2SQwb1T9bZxYmTp6Gjo8OZU/+wc7tyu2vuPHno00+5Nbd/v16EhoYmXK+jo5PQUmH5Mi8aNW6KhYUF9+7dxXPIINx79aZO3XpERkbi0rQhLVq34ZWeHl2l0kQTwBigq1SKj54effsP/O51V6yobDD/rXVD46bK3m2HDh2gcdNmaGtr8+jRQx4+ePDdmLly56ZqteooFAo2/qt3Ybf4/okH9u/lw4ekt0JaZ89O0/iE02tR4sVXuvXoia6uLrduXufKpQtJjpsccrmc3v2UZyu9Fs5N1Wp09Zq1KVS4KOHhYWxYvVQlcaWVVCpN+D3bvGoxERGq2SL9K9ntHKjdUNm+5+QGzRSbEQTh7yGSP0EQUqxly5bMnDmT0aNHU6xYMby9vTly5MgPRWDUpVaHPsjkWly9cJrrl86qfT4tbW269VOuSnjNn0nQl0C1z5kc7Tp2w8o6O+/fvWXl0kUpvl8ulzNijDKB9lo0n7dvU3cW879KlS5LE5cWKBQKPAcNSHR1afS4iRgaGnLt6hU2bki6oI69g0NC8Zchg/oTGKj8OXiOGIWdvT1v37xhxLAh391TuUrVhGIogwf0Y+oMZUERr8UL2bJpI6vWbiBf/vy8f/eO7l3cWLFxC/sNDSmnpcU6SDgDGAGsA8ppa3PAyIjdh49jZ2f33Vy58+YFSFi9c6pcBblczts3bwgODqZqteoAHPtJo/W27ZSJ8PatWxK+XwULFaJsOUdiY2PZunljkt8fgJ7xZwV37dhGQEDAT6/JbGFBy9ZtAVi6RHVbC1u360DmzBa8fe3DwX0p31IqkUjoFX8mcd0KLyJUdBY1reo3aYG1jS2fAz5xYEfyfg5p1aGHMpG+e/YoH18lfS5WEAQhuUTyJwhCqvTu3RsfHx8iIyO5cuUKZcuW1djc5lbZKddAeS5m0YxxKtu69iu1G7UgR+78hAQHsTSDVCTU0dWl/1BlMZF5s6YREOCf4jGc6zagXAXlNs2JY0aqLLaxE6agq6vL+XNn2LXj50VpslpZMXS48szfyOFD+fw56a1+AwYNJU+evPh+/IjnYGWiYGBgwOKlKwBYvnQJx45+X/Bk0pTpFCxYCF9fX1atWJbQfL1nj67cu3uHvQeOYGNry5PHjxno0YdNO/dStlsP+ujrYySRYK6lhZFEQh99fcp27c75G7cpVbr0D7Hp6ihrhUZGKQsD6evrky9ffgDu37tLlfjk78L5cz/cW79hI7S1tXny5PF3xWu+bf3ctnVzkt8bUFZTLVK0GJGRkb9MGLvHJ8QH9+3hYzJWFZNDT08Pt/hzh8sWp+7cXoPGLmS3teNzwCf2bFdNRdK00tLSorO7srXIhhULUrWqmVI5cuejcs16AJzavEzt8wmC8PcQyZ8gCL+lGu17oa2rx/3bNzh9bH/SN6SRTCaj12BlorV2+SI+vH+r9jmTo5FLa/IXKkJIcBCzpqZ8G6xym6ayMue2LRu5fu2KSuKysbWjX3xPvxGegwkJCfnpde69+5IvfwH8P31i5PAhP73m33R0dFiybCUSiYQN69ZwcP8+AKpUrYZ7b+WqV7fOHb5rO6Knp8fGLTswNjbmwvlz+Pn50rBxEyIjI2nWuAH+nz5x7MRp7B0cePH8Oa1aNKVW7Tq8eO/H3sPHWLxxC3sPH+PFez9mzZ3/w4rfN99WTi0sLBOes8+RQ/m1N28oVboMAN7eP1ZxNDY2xqlKVYDvqnU2atIMmUzGbe9bP/Qz/BmJREJHt84AbFy3JtHrChUuQtly5YmJiWFTKs7oJaZzV3e0tLS4ce0Kt26k/EyuXC6naw9lYrp6+SKNfLCTHM1bd8AsU2bev/Hh1FH1/30D0NFdufp38/g+Av3ea2ROQRD+fCL5EwTht2ScyQKn5sozhotnTtDIp/EVq9WmaClHIiMjmDdtgtrnSw6ZTMawMcrKp2tXLuXJ44dJ3PGjYiVK0qJNewA8B3mkqnfgz/TtPxiHHDl5/+4dk8aP+ek12trazFuoPNe0dvUqTp/6J8lxyzmWT+jd17N7l4TzcBMmTaVgocL4+fnRoV2r7/5M5MmblzXrNyOVSlm3ZjX58uWnYiUngoODqVe7Bn5+fpw6e5FSpcsQGBhI4wZ1GTFsKKVKl6Fxk6ZUq14jobjLz8TFxXHooDIpKFPm/6vgxkbKyrYhoSEJq4Dv3r4lIuLHphLVq9cE4Ozp0wnPZc6cmQqVlGcJv42flOYtW6Otrc3dO7d5cP9eotd17KysMrpx3RqVJVmWWbLQuGlzAFavSN15tTbt3TAwNOL5k0ecP3My6Rs0QE9fn3Zu3QDYsHy+RpLSgkVLUrJcJeJiYzi7bbXa5xME4e8gkj9BEH5bVVt3w8DEHJ8XT9m/fYPa55NIJPQbpkz6dm7dwKP7GaMSX3mnqlR3rkdsbCxjkrF69jMjxkzE0MiIm9evselfRUfSQk9Pj+mzldv/vBYt4GYiK0GOFSrSuVsPQJnM/btoS2LGjJtI4SJF8ff3p3PH9sTGxqKnp8eGzdswNDTk3NkzDPcc/N09tevUZfY85Rm36VMnU71GLRzLV+DLly/UqVWNWzdvcOLU2YS2DUuXLKJIgTx4LV6UZEGduXNm8fTJE4yNjanfsFHC8xGRyiRPR1uHTJkyoaWlBcAnP78fxihfsRIAV69c+i65cK5dB4CTJ44n+X0BZZ/AmrVqAyQUxvmZxk1dMDQ05OWL5yor/ALQOb6y6b5d2wlMxlbe/zIyNqZ1/BnIdalMINWhnVt3dHR0eXj3FreuXdTInK7dlNtNrxzYylcNtJoQBOHPJ5I/QRB+W7oGRtRw7Qko+/6FhyWdNKRVoWKlqFG3CQqFgiljh2WYbWnDxk5BS0uLUyeOcuzIwRTfnyWrVULrh3Gjh6XqTfvPVK/pjEuL1sTFxdG7R1eioqJ+et34SVOxtbXDx+cVw4YM/Ok1/6ajo8Pa9ZsxMDDgzKl/mDR+LKBc4Vu2cg0AC+fPZfWqFd/d1627O6PHKhP4cWNGUr1GTWrUrEV4eDguTRqyaOF85sxbwMEjx8mVOze+vr7079ebXPbZ8ejTi8OHDuLn54dCoSAqKorr167Rxa0DIzyVSff4iVMwMjJKmO9V/FZN6+zZkUgk6OnpAfx05a9w4SLIZDICAgL48P7/2/yqVFWeFbx44VyyG7M3dVGuvu3dvTPRawwMDGjYWFk5d3syzxQmR+ky5ShUuCgRERHs3Ja6c3tuXZUfBpw+cYS3r31UFltaZMpsQePmrQFl3z9NKOdUnZx5ChD5NYxL+1X3MxIE4e8lkj9BEH5r5Ru1JZO1LQGffNmwXDPNoXsNHoOWtjYXzv7D6RNHkr5BA+xz5MKtu/LM26ihA3+aXCSlS4/e5M1fgAB/f8aNHq6y2CZPn415pkzcu3uHmdOm/PQaIyMjFi9T9lFbtXI5hw4kvcUxb758Ca0cpk2ZxP69ewBo1KQpI0Ypt5n27dXjhwIwnsNHMiK+Gf3E8WPJly8/Hd06ExcXxwjPIbg0aUihwkW44X2PufMXYWdvz+fPn1nqtZimjepjZ50FIz0tTAx0qFS+TEKl0uEjR9Oth3vCPAEBAdyOb3VRvERJFApFwgrityTw33R1dXFwUJ4RfPr0ScLzhYsUwdDQkJCQEB4/fpTk9wWgTt36yOVynjx+xPPnzxK9rnlLZTKzf88ulW2dlkgkuCacO1yVqg9IcubKQ+WqNVAoFGxZr5n+esnRsZvyPOLZE4d49+aV2ueTSCS07axciT6/ax2xMdFqn1MQhD+bSP4EQfitybW0qddVub1v3fIF+H1Uf2EEa1t7WnVUvsmfPMYz0dUsTevZfyhZslrh8+oFi+bNTPH9WlpaTJ2l7A+3bvUKLqtoK2BmCwumzVIm5jOnTcb71o8FTwCcqlSld3zPvu7dOn23+pWYlq3a4B7f3qBzx/bcvXMHgGEjR9O6rXI7aJuWzbhy+dJ3940YNYbJU2cAsHDBPAICApg+cw46OjocOniAEkUKsG3LZrp278H9R8/Ye+AwnTp3JVfu3EgkkoQVOGNjY5q6NOfU2YuMGjMOiUSSMMfypUuIjY2lWLHi2NnZ8eHDB6Kjo5FKpVgm0hbFxtYWUJ4L/EYmk1GkaDEAbnvfSvJ7AmBiYpKwjfT40cQ/oKhctRrmmTLh7/+JSxd+rEKaWi4tWqOjo8PD+/e4k8yY/8u1U1cAtm9aR3R0xkh6cufNT4XK1YmLi2PH+hVJ36ACtRq4kMkiC0GfPnL71I9tQgRBEFJCJH+CIPz2ilSpg32hEkRFfNVY43e3ngMxz2TBy+dP2bAqYzSkNjQ0YthYZYP1ebOm8erF8xSP4VihEq3bdQSgfx93IiMjVRJbU5cWNGzSjJiYGLq6uSZ6hm7M+EkULVaczwEBuHVom6zVqCnTZlK5SjXCwsJo1rg+79+9QyKRsHjpcqrHb+ls3KAON2/e+O4+jwGDWL12I9ra2uzft4dVK5exZv0mChcuQkBAAF07d6RyRUfOnjlNzVrOLPJaxt0HT/gcHM5zn3e8fu/HR/8vbNy8jXKOjt+Nfdvbm+lTJyvnGaj8cOLaVWUl1Tx58qKtrf3T15IpU2YAAgO/33ZboGBBAB4/Sn5Bnxo1awFw+p8TiV4jl8upW68BQELlVFUwNTOjbgPl2ccdW1PXG69WnfpYWGYhwN+PU8cPqSy2tOrQRfnBz/4dG4j4Gq72+bR1dHBpq1xJPbtjdYbZai4Iwu9JJH+CIPz2JBIJDXuNAODgrs08vOut9jkNjYzpMVDZo27ejEkEfPqxgEd6qNfYhfKVqhIVGcmwQf1S9UZx9ISpZLaw5PHDB8ye8fNtmiklkUiYNXcRWbJk5fGjh4z4TzGWb3R0dFi1flNC0ZaJiVQJ/TctLS02btlOnjx5eff2LU0a1iMoKAhtbW02b9tJ+QoVCQoKon7tGly/fu27e1u2bsPRE6exypaNRw8f4ubalvYd3Rg3cTIGBgZcv3aVus41qFS+LBvWrSUkJARdXV2yZcuGhYXFdyt93xw6eIA6tarx9etXatZypkVLZU/Kvbt3AST0+/sZXd34XoH/SbodcuQE4OXLl0l+P76p+u2s4Plzv6zgWq9BQwCOHTmo0sTiWyP53Tu2pmpLqZaWFi1atwNg+0bVFCFShcrVnbGxcyA46AtH9+/QyJxN23RCrq3Nm0d38LmfupVUQRAEEMmfIAh/CLsCxSheoyEKhYLZEzVTiKWBS1vyFSpGWGgwMyaOUvt8ySGRSBg3bS5a2tqcOnmMvTsTr/aYGDNzcyZNnwPAnBlTuXfntkpiy5Q5MwuXKs9vrVi6hEMHfr7SlDt3HubHn+WbMW0KB/btTTpmMzN27zuEZZYs3Lt7h+ZNGhIeHo6BgQG79h2knGN5vnz5Qj3n6pw7e+a7e8uWc+TS1VvUqOVMREQEQwb25+jhQ+zcc4AePXujo6PDjevX6Nq5IzZWFjRuUJfpUydzYP8+rl+7xm1vb/45eYK5c2ZRpVJ5mjVuQGBgIKXLlGXdxi1IJBJePH/Oju1bAWjdtn2ir+Pb9ka5XP7d89bW2QHw/Zj8huxFihZDX1+fL1++/HLFsHLV6mhpafHq5Qte/OJ8YEpVrV5LuaX0kx8Xzp5O1Rit23cE4Oyp43zy+/jrizVEJpPRpoOyTcbODSs18neNWabM1GmoLOJzbmfGSYQFQfj9iORPEIQ/Rv3uQ9DS0eX29UucOLRH7fPJZDIGjVE2SN+xZT23rl9V+5zJ4ZAzNz09lNUnR3oOTFXlzoZNXKhbvxExMTH06t5ZZWeuqtd0pmcfDwB6dO3Em9evf3qdS4tW9Ig/y9elkyuPHia93dHewYG9B45gYmLChfPnaOnShIiICIyMjNhz4DBOlasQEhJCw3rO7N75/YqNpaUle/YdYva8hRgYGHDxwnnq1a5BbEwM5y5eZdyESeTKnZvIyEiOHjnMmFEjaN60EZXKl6Fc6eLUq12TYUMGceXyJbS1tenXfyDHTp7G1NSUqKgounbuSHR0NDVqOVM6vtn7zwR+CQTAxNT0u+fNzM2VXw8MTPL78I1cLqdEyVIA3PzPiue/GRoaUrZceQDOnFJdXz0tLS0aNFJWE923O3UrZLly56Vk6bLExsayb1fKP8hQl2at2qOtrcOj+7d5eFczK3EtXJV9Bu+cOUJwQMbYaSAIwu9HJH+CIPwxTC2tqNqmOwDzp4zSyHmcIiXKUL9ZGwDGDvNIdil+devWeyC58ubH/5MfY0b8fIvlr0gkEqbOXoCZmTl373gzc9oklcU2evxkSpQsxZfAQDq0a5VowZxJU2dQoaITISEhtGjWiICAgCTHLlKkKDv3HMDAwIB/ThynpUsTvn79ipGREbv2HaRhoyZERkbStnVzZkyb8t2qjVQqpYd7L27efkCjxk2JjY1l+TIvKpUvw5vXr9m2Yw/Xb91l2ozZtGjVmuLFS5DdxoasVlbkzZeP+g0aMnX6LB4/92Hq9Jno6uoSHBxM6xbNuHjhPEZGRsydt+iX8fvEb+v8ttL3zbfqoJEprOJarHgJgISqo4lxqlIVgAvnz6Zo/KQ0atIMgMMH96W6mqhLS+X20X07t6gsrrQyz5SZ2g2aALB78xqNzJm3YFGKlChLXGwMl/dv1cicgiD8eUTyJwjCH6Va626YZbXG98Nb1nrN0cicvYeMw9DImPt3vNm0drlG5kyKjo4Ok2ctRiKRsG3Tek6dOJbiMSyzZGVKfJXO2dOncPNG4qtHKaGtrc3KdZsxMTXl+tUrifb109LSYv3mbdjZ2fP8+TPatnJJVmVVx/IV2LF7P/r6+pw4dpRmjRsQGhqqbAK/ZRvuvZTl+seMGk7H9m1+aCpvY2vL5m07OXriNI7lKxAZGcmK5UspUbQgvdy7IZVKGTN2AheuXOfpi9e8fP0e77sP2b5rL/36DyBr1qyEh4ezdvUqShYrxKGDB9DR0WHT1p3kyJkz0bjDwsISWjwUKFDwu699S1J/dsbwVwoULAQkXSimQnxl0MsXVdfsHaBCpcqYmZvzOcCfq5dT1xi9YVMX5HI59+948+LZk6Rv0JBW7TsBcOzATsJCQzQyp0t75XbTywe2EKui1hyCIPxdRPInCMIfRUtHl4Y9lT3q1i6bx7vXr9Q+p3lmC9zji7/Mmjw2w5xNKlG6LB269ARgUD93QoKDUzxG42YtaNysBbGxsfTo3IGwsDCVxGZn78DSlcqzS8u9FrNx/c/PMWW2sGDrrr0YGRlx7uwZ3Lt3SdYZK6fKVdi97xCGhoacOfUPdWtVx9/fH5lMxsw585m7YBFyuZzt27bgVL4M9+/d+2GMSk6VOXHqHEdPnKZ+g0ZIpVKuXL7E4IEeFMyXixx21jRuUBePvr2ZMG4ME8ePpX+/PtR1roGNlQU9unXm7Zs32Nnbc/TkGarXqPnLmM+cPkVcXBy2dnZks7b+7muhIcrkwsDQMMnX/m+5c+cB4MWzX5/lK1GqNDKZjA/v3/H+/bsUzfErWlpa1HKuC8CxwwdTNUamTJlxqloDgIN7NVNgJTlKl6uAQ87cfA0P4/jB3RqZs5pzQ8zMMxP06SMPLqpui64gCH8PkfwJgvDHKezkTO6SFYiJimL2RE+NzNm0TSfyFSpGaEgwk0YN1cicyTFg2Fhs7Bx49/YNY4anfPsnwJSZ87HKZs2zp08YMfTnq3SpUat2PQYPGwmAR293rl/7+ZnJAgULsXbTVmQyGVs2bWDMqOQ1oK9YyYmDR05gbm7OjevXqO5UgRfPle0vunZ358iJU2S1suLRo4dUdCzF4oXzf6iKKZFIqORUmW079/D05Vumz5xDJafKaGlp8fHDB44eOczSJYuYPHE8kyaMw2vxQk79c5Lw8HDs7O2ZPHUGN28/oEyZsknGu23LJgDq1qv/w9d8fZUfKFhYWCbrtX9jb+8AwNu3b365JdnAwIB8+QsAcDuRPoyp5VxX+XpOHkt9u4aGTVwAOLxPM0lWckgkEpq36QDAgR2pa2eRUto6OjRorqyAemn/Zo3MKQjCn0Ukf4Ig/HEkEglN+o5GKpNz7uQRzv2TeJNrVZHJZAybOBepVMqBPds5e+q42udMDn0DA6bNW4pEImHT+tWcOJbyJtFm5uYs8FqFRCJh3eoV7NuzS2XxDR0+mtp16xMZGUmbFk15/+7nq041ajqzIL4C6KwZ05g/d3ayxi9VugwnTp3HxtaWZ8+eUqViOS6cVzYzdyxfgUvXblHTuTaRkZEMGtCPOrWq8ezp05+OZWVlRe++Hhw9cZqP/kGcPH2e+Yu8GDRkGN169KRrd3cGDRnG4qUruHrjDg8ev8BjwKCE83q/8trHh927lKta7Vw7/vD15/Erd3Z2dsl63d9kyZo1oSm9/6dPv7y2cJGiANy7q5rqrt9UrVYDmUzG0yePee3zKlVj1K7bALlczpNH93n5/Oc/n/TQuHlrpFIpd25eweeFZuJq0qojAE+unSfgwxuNzCkIwp9DJH+CIPyRstjnonIL5ZmcmeOGaKT4S/7CxRIq8o0Z0o+v4eqfMznKOFakYzflObcBvbvz+XPShVP+q2LlqvT2GARAv57dUv0m/r+kUileK9eRL39BPn74QCuXxoluLW3XwY0x45WFZ4YNHcTa1SuTNUfefPk4dfYSxUuUJCAggHrONVixzAuFQoGlpSW79x1kzvyF6Ovrc+7sGUqXKMyEcWMI/8XPT09PD8fyFejStTvjJ05m7vxFzFuwmPETJ9PRrTOFChdO9vk8hULBsKGDiI6OpnLVahQvUfKHa7y9lRUlCxYqnKwxv5HJZJjHVwoNCPD/5bUJ5wOTUVk1JUxMTSkVv/J5NpXVRE3NzKhQqQoAxw/vV1VoaWaZxQqnasrtvId2a6YIi7WtPWUrVkWhUHD10HaNzCkIwp9DJH+CIPyxarr2xsQiKx/evmb14uStFKVV9/4jyGKVnTevXzFvxkSNzJkcA4eNJWeefPj5fmRwv56p6k02ZMRYSpQqQ1DQFzp3aJOs4ivJYWxszOYde8ic2QLvWzfp5Nom0S2KAwYPpW9/5dbTXu7d2LxpQ7LmsLKy4tjJMzRzaUF0dDT9evekW2c3wsLCkEgkdOvRk6s371C9Zi0iIyOZMmk8RQvlZe2aVamuUplca9esYveuHchkMiZPnfHD16OiohIKsZQp55ji8Y2MjAEICfl1UZI8efMC8Oyp6ouqOFWpBsD5s6dSPUbtespm9CeOHFBJTKrSpLmyGumRvVt/2DasLg1buAJw7fBO4jJIhWFBEH4PIvkTBOGPpaNvQOO+owFYt2weL589VvucBoZGDBk/E4BVXvO5d1u156dSS1dPj1kLVyCXyzm4bzdbN61P8RhaWlp4rdqAiYkpN65dZexI1Z2ntLN3YMO2Xejo6HD44AEGD+j30wRVIpEwYfI0OnfrgUKhoFvnjmyNPyuXFH19fdZu2MyESVORSqVs2rAOJ8cy3Lmt3ObokCMHew8cZsPmbdja2fHu7Vvcu3WmRJECrFu7msjISJW93m9279xBn57K9iQjRo2hWPHiP1zzz8kThIWFkSVrVgoXLpLiOXR1dQGISiJ+hxzKSqSv1VAkyamyspXExfNnU90UvVadegB437jK5yRWMTWpunM9DAyN+PDuDbdvXNbInJVr1MXY1IygTx95fE217TkEQfizieRPEIQ/WuFKtcjvWJXYmGimjR6Q6jeeKVGpWm1q1W9GXFwcnh7uKmuQnlaFipag3xBlVdIRgz14+fzXFSB/xtbOnvleyu2WXovmq/T8X5myjnitXIdEImHF0iXMmDr5p9dJJBJmzV1AB7fOxMXF0cXNlQ2JVAv92b0DBg3h0NGTCcVeKlcoy+yZ04mNjVWeF23mwq27D5k0dTqZMmXi2bOn9Ojaiby57Bg/djSvfXzS/FojIyMZM2oE7dooK6m2btuewZ4/L2SzdpXy+920WXOk0tT/s53Un/3sNrYAfAkMVFlV129Kli6LtrY2fr4f8Xn5IlVjWGe3oUChwsTFxXH+dMapdKmrp0ft+o0AOLJXM9swtXV0qNOoBQBXD+3UyJyCIPwZRPInCMIfTSKR0LTfWLR19bh55QIHdmqmKt+AUVMxMTPn0YO7eM3/cStfeunWewBlylciLCyU7p3apWrrpnPdBvTsOwCAXt07JdlDLiUaNWnG1JlzAZg4bjQrl3v99DqpVMq8RV507NSFuLg4undxY5nX4mTPU8mpMpeveVOvfkOioqIYNdyT6pUrJrR80NXVxWPAIO4/ecHEKdOwypYNP19fpk6eQL7c9tSs5sTC+XN5+uRJij5QCAsLY83qlZQoWoAZ0yajUCjo0bMXS1es+mli9/DBA/bv2wNApy7dkj3Pv337Gevo6PzyOiMjI/T19QHw81VtuxJdXV2Kxjecv3b1UqrHqVbDGSDDFFT6pkHTlgCcOrqPGA192POt6uf9iycJD/6ikTkFQfj9ieRPEIQ/nrlVdmp17AvAzIkj+Oz/66qHKpkzswUDR08DYNGcaTx+8GMfufQgk8mYuXAlJqZm3PG+yeRxo1I1zvAxE3Gs6ERYaCiurV0ITkUPwcR07dGLgUOVq2AD+vZOaIHwX1KplLkLl9C9p7KYTf9+vZk2ZWKykzELCwu27tjNkmUrMTY25trVK5QvU4IRnkMSzscZGRnRf+BgHjx5wdoNm6lSrToSiYQL588xZFB/ihbKS+4cNrRt1Zwpkyawbctmzp09g/etW9y7e5erVy6zd89uZkybQvOmjbCztqRn9y68fPGCrFZWbNi8jVlzFyCTyX6IT6FQ4DlkIAqFgoaNmvzQ+D25goODADA0MkryWnPzTACpKgqUlFKllUVfbl6/luoxqsQXV7l49h+NrOInV7kKlTHPZMGXzwFcu6SZbZh58hcmd/5CxEZH4f1P6nooCoLw9xHJnyAIfwWn5m5ky1WAryFBzJ44TCNzOjdwwalGXWKioxnSr1uG2f6ZzTo7U+cqV9S8Fs7h2JGUv3GUy+UsW72RbNbZefrkMe5dOqi02MXwUePo3M0dhUJB984dE91eKpVKmT5rLkPi+wWOHzuaAf16/7Kn3b9JJBJcO7hxw/s+DRo2JiYmhrmzZ1K0YF7Wrl6ZMI62tjYuLVpy8MhxHj/3YdrM2ThVqYq2tjbv371j964dTBg3mo6ubXCuUYXyZUtQpmQRqlRypHWLpowZNZyDB/YRHh6OQ44cTJo6nTsPntCkmUuisS3zWsyJY0fR0dFhwqSpKfwOKkVHRxMQoEzkMme2SPJ6YxMTAEJUmMx/U6JkaQBu37qR6jFKlXVER1cXP9+PPHvySFWhpZlcLk/Y+nny8B6NzVu3SSsArh/NOP0PBUHI2ETyJwjCX0Em16LF4ElIpFKO7d/BhVPH1D6nRCLBc8JsjE3NuH/HmyXzpqt9zuSqWacBHbv2AqBvj868eZ3yc2wWlllYuX5bfJGW/UyZMEZl8UkkEqbNmkfrtq7ExsbSsV1rDu7fm+i1I8eMY9qsuUgkEpYtXULrFs1SdG4tm7U1W7bvYseufeTIkRPfjx/p2b0rZYoXYef2bd8lttbZs9O7rweHj53knd9nDh//h4lTptHOtSMVKzmRJ09eslpZYWFpia2dHaVKl6F5y9ZMnDKN81euc/fhUzwGDMLAwCDReI4dPcKQgf0BGD9xCrly5072a/m3d2/folAo0NbWxsIy6QbxuvE9CSMjI1I1368UKaYsZvPw/t1kJ+f/paurS+kyyoqnVy5mrEIndRo0BeDM8YNqrxD7jXMDFyRSKT4PbhHwXvT8EwQhaalK/hYtWoS9vT26urqULVuWq1evJuu+LVu2IJFIaNy4cWqmFQRBSBObfEVwcnEDYOqoAYSF/rr0vSpktszK4DHKM3+L5kzj3p1bap8zuQaPmkjhYiX4EviZbh1T17qheMlSzJy/BIBZ06ewc9sWlcUnlUqZv2Q5Li1aExMTg2ublhyIP//2M+69+rBu01Z0dHQ4eGAfNas58e7t2xTNWadefa5732PKtJmYm5vz6NFDXNu2omSRgqxZtYKIiO+TIn19fZwqV6H/wMEsXbGKoydPc+veQ577vOPV2488fPqSMxcus2b9RvoPHEzx4iWS7P+3a8d2Wrk0ISYmhpat29KrT78UvYZ/e/JEWeE2R85cySoW8237aWys6lsW5MiZC11dXb5+/YrPq9QVfQFwrFgJgOuXL6oqNJUo7VgRM/NMBAV+5uaVCxqZM7NlVspUqALAndOHNDKnIAi/txQnf1u3bmXAgAGMGTOGmzdvUrRoUZydnfHz8/vlfa9evWLQoEFUqlQp1cEKgiCklXMnDzJls8X3w1sWTh+rkTlrNWhGtTqNiI2JYVDvLkRGqH5VJTV0dHRYsHwjxiam3LpxjbEjhqRqnOat2iUUgOndozPXrqqu3L1MJmPx8tU0dWlJdHQ0rm1asmvHtkSvb9SkGQeOniSzhQW3vW9RsXxpLl9KWZKgo6NDX48B3Hv0nBGjxmBqasqTJ4/p1aMbeRxsGO45mMePVL/lMDQ0lIEefWjfpiWRkZE0bNQEr2Urk90s/mdu31Z+2FCgUKFkXf9tRU4qTf2ciZHJZOTNVwCAxw8fpHqcso4VAbimoQQrueRyOdWdle0ozhzXXC9C5wbKrcPep49obE5BEH5fKU7+Zs+eTdeuXXFzc6NAgQJ4eXmhr6/PqlWrEr0nNjaWtm3bMm7cOHLkyJGmgAVBENJCR0+f5oMnAbBz40puXD6n9jklEgme42djntmSZ48fMnOy6rZHplV2WztmLVK2Eli1bDE7tqauGuqIsZNwrlufyMhI2jRvgs+rlyqLUS6X47VyLc1btiEmJoZOrm3ZuG5NoteXLefIqXOXKVioMH6+vtSuWZXlS5ekuECIiYkJw0eO4eHTV0yaMh0bW1sCAgKYN3sWJYoUoGK50syaMY2HDx6kqfhISEgIixfOp0iBPHgtXgRAX48BbNi8DW1t7VSPC3Dx/Hng/8VWkvLtgwkdHd00zZuY3HniG8k/SX3PzeIlSyOTyfD98J7371K2sqtuNes0AODcycMaK0hTpVZ95Nra+L9V3e+cIAh/rhQlf1FRUdy4cYMaNWr8fwCplBo1anDpUuKlm8ePH4+lpSWdO3dOfaSCIAgqkrtEeco1UBZKmDisD1/DVdvT7GdMzTMxcuoCAFYvXcDFs6fUPmdyVa1Zh179hwIwqF9P7t3xTvEYyhW6dRQqXJQA/0+0aNqAL4GBKotRLpezePlq2ndU9vZz79aZhfPnJnq9nb09x0+fp3HTZkRHR+PRtxed3VwJDQ1N8dzGxsZ4DBjEvYfP2LZjD3XrNUAmk3Hr5g1GjxhGqWKFyJvTjk4d2uO1eCEXL5zH398/0Tf/MTExPHzwgLVrVuHaphU5bKwYPMAD348fyZEjJ3v2H2bKtJk/rQCaEhEREVw4rzwX51S5SrLu+VboxcjYOE1zJyZHrlwAvEplrz8AAwMD8hdQrmTeuXVdJXGpSvlKVdHR1ePj+7c8fXhXI3MaGhlTsUotjcwlCMLvL0XJn7+/P7GxsWTJkuW757NkycLHjz/vCXT+/HlWrlzJ8uXLkz1PZGQkwcHB3z0EQcgYJk2aRPny5dHX18fU1DS9w0m1Bu6emFpa8e71KxbNGKeROStWdaZJa+WZw8F9u/Il8LNG5k2OvoNH4lStJhFfv+LWtgUBAf4pHsPA0JD12/YoK4A+fkTblk1+OCOXFjKZjLkLvejZxwOA4UMGMnqEZ6JJlqGhIWs3bmXilOnIZDK2bt5IJcfS3L7tnar55XI59Ro0ZPuuvTz3ec+8BYupUdMZHR0d3r19y9bNGxno0ZeaVZ2wy2ZJFnNjCufPjWPpElRyLEPZksXIm9OOTMb6lCpWiJ7durBzxzbCw8PJmzcf8xYs5sbt+9Ss5ZzK79D3Th4/RlhYGNbW2SlcpGiS1ysUCvzj26BkypRZJTH8l52dAwCvfV6laZzi8ZVD76Shcqg66OnrU8GpKgDnNVBU6pua9ZpqbC5BEH5vaq32GRISQvv27Vm+fDmZMyf/H5IpU6ZgYmKS8LCxsVFjlIIgpERUVBTNmzfH3d09vUNJE10DI5oPngzAtnXLNLL9E8Bj+ERsHXLh++E9Iwb1zjC9ymQyGXOWrMHWPgdvXr+iW4c2qWpNYZXNmo3b92JkbMylC+fp3tk11ZUdf0YikTBhygxGj1Nu3Z07awZd3VwTLVYjkUjo238gB4+eJJu1NU+ePKZKxXLMmzMrTa0pLCws6NKtB3sPHObtxwD2HzrGsBGjcK5dl+zx/2aFhYXx4vlz7tz25uaN69y7e4e3b94QExODgYEB5StUZPDQYZw+d4kbt+/TpVuPNG/z/LeNG9YB0LiZS7LODX758oXw8HAAsmS1Ulkc//bte/P+XdoqUxYuqqwcev+ud1pDUrmqNWsDcPG05hrRV6haC5mW6v7sCILw55IoUvDOIyoqCn19fXbs2PFdxc4OHTrw5csX9u79vgy3t7c3xYsX/27ryrd/bKVSKY8fPyZnzpw/zBMZGUlkZGTC/wcHB2NjY0NQUBDGatqKIghCyqxZswYPDw++fPmS4nuDg4MxMTFh0iFvdA2SbjytTttnDOfyga1YZbdl08ELGBiqP56Hd73p3LwmMdHRTJq1iJbt3NQ+Z3I9efSA5nWrEBYWiltXd6bMnJeqcc6fPU2bZvWJioqiU9cezJizIE2FS35m84Z19OvVjZiYGCpWqsyGrTswNzdP9PoAf3969ejCoQP7AajkVJklS1fioIaz6F+/fuXtmzf4+38iJCSE2JgYtLS1MTU1xcoqG1bZsiWr+mZqvfbxoVD+XMTGxnLl5h3yJ6NB/M0b16lSoSyWlll49PKdWuJ69vQJZYoVwMDQkOfvUr/yffP6VepWr0imzJZcuf9KdQGqwPu3b3AqmRepVMqx6y8wNjHVyLzXLp6hV/tG4r2SIPwhvr1XUvXvdIr+5dHW1qZkyZKcPHky4bm4uDhOnjyJo6PjD9fny5ePu3fv4u3tnfBo2LAhVatWxdvbO9EVPR0dHYyNjb97CIIgqEODXsMxy2rNh7evmTd5pEbmzF+4GO4DRgEwfsSgDNWsOk++AsxcpKwwuXr5EtasWJqqcSo6VWHB0tVIJBJWLfdi6iTVb61t3c6VLTv3YWhkxPlzZ6juVJ6nvygkkilzZjZv3828hUswMDDg3NkzlClZhMUL56t0dRJAT0+P3Hny4Fi+ArWca1OnXn1q1KxFqdJlsM6eXa2JH8DM6VOIjY2lStXqyUr8AB7FV+DMlSeP2uKytFQeGwkLDeXr16+pHidv/oJIJBIC/P0IiN+qmlFky25Dzjz5iIuL49rFMxqbN3/h4hqbSxCE31eK//UZMGAAy5cvZ+3atTx8+BB3d3fCwsJwc1N+cu3q6sqwYcMAZTPWQoUKffcwNTXFyMiIQoUKqXR7iyAIGVdGPserq29IK09l8/U9W9dqpPk7QNsuvSlToQqREV/p182ViDS8EVa1mnUaMGDYWABGDPHg7KmTv74hEY2aNmfKzPkAzJgykcUL5qoowv+rVqMWR06cxcbWjufPnlK1kiPHjyVe8l4ikeDWpRsXr3lTsVJlwsPDGTzQg6pO5fH2zjg9GNPiwYP7rFmtrODqOWJUsu/zvnUTgEKFi6kjLEBZSEYulwMQ+Dkg1eMYGBhgY2sPkKE+PPmmUhVlYbwr5/5J50gEQRC+l+Lkr2XLlsycOZPRo0dTrFgxvL29OXLkSEIRmNevX/PhwweVByoIgvp4enoikUh++XiUhr5mGf0cb67i5XBq3glQVv/8koY3pckllUoZO2sp5pksePzwHpPHeqp9zpTo0XcQjVxaExsbS2fXVjx+lLq+bB27dGfoyLEAjPQcxNrVK1QYpVKBQoU5ceYSZco5EhwUhEuj+syeMe2X5ykdcuTgwNETzJ6/EGNjY25cv0Ylx9L079uLz58zTiGelIqJiaFPz+7ExsZSv2EjyldMfm/dK5eVVbtLlS6jrvCQSCSYxBeKCg4OStNYufPmA+DFs9S3jVCXb0Vfrl48nb6BCIIg/Eeq9p307t0bHx8fIiMjuXLlCmXL/r9/0OnTp1mzZk2i965Zs4Y9e/akZlpBENRk4MCBPHz48JePtPToHDZsGEFBQQmPN2/SVuxBHep2HUgW+9wEfPJlykgPjRRiyWyRhTEzvQDYtGY5h/btUvucySWRSJg8ezGlypYnJDiIts0b4ef786rOSfEYNAz3Psom8AP6uLN10wZVhgqAhaUlew+doH3HzigUCsaOGk7bls1+eSZVKpXSpZs717zv07R5C+Li4li2dAmFC+Rm4fy53509/11MmTSey5cuYmRkxLSZc5N9X2BgILfjV/4cU5Awpoa+vgEA4WFpa7GSI2d824gXz9Mck6qVdqyITCbj/Rsf3r/1Se9wBEEQEqj30IEgCL8FCwsL8uXL98tHWrZp/w7neLV0dGkzYiZSmZxTR/dzYGfqmp2nlKNTdTq6KxOjYf3defUy47yR1dHRYfHqLdg55OTtax/at2xCWCresEskEkZPmELHLj1QKBT06t6Jndu2qCXeeYuWMnvBErS1tTmwby9OjqW5dfPX7QCssmVjzfrNHDhygoKFCvMlMJChgwdQvHB+Nm5Yp/LzgOqyfdsWpk6eCMDs+YuwsbVN9r3HjhwiLi6OvPkLYG2dXV0hAqCrpweQ5jYgdg7KD6Te+GS85uaGhkYULlYSgJuXz6dzNIIgCP8nkj9BEFLk9evXeHt78/r1a2JjYxOKOaWmeXZGkz1PIWp37g/A9LFDeauhN5XdPIZTtJQjYaEh9OnSNkOd/zPPlJmVm3ZjZp6J27du0N2tLTExMSkeRyKRMHnGXNq6diIuLo7unV3ZuX2rGiKGjp26cvjkWWzt7Hn18gU1Kldg4fy5SbZ2cKpSlfNXbjB/kRdZrazw8XlFt84dKVm0IBs3rEtV6wtN2bd3N13cXAHo2acfLVu3TdH9u3duB6B+g0Yqj+2/5DLlmb/YVPw5+jdbWzsA3r19neaY1KGMo3IF9ebVC+kciSAIwv+J5E8QhBQZPXo0xYsXZ8yYMYSGhlK8eHGKFy/O9evX0zs0lajaqis5ipYh8msYowd0JUYDb/jlcjmT5q3EzDwzD+/dYfyIgWqfMyXsc+Ri6bod6OjqcuLoIYZ49ErVtlipVMqMeYtp3a6jMgHs1J7tWzapIWIoXqIUpy9co37DxkRHRzN8yECaNarHxyTOpMtkMjp27or3/SeMmzgFM3Nznj59QrfOHSlSMA8L5s3JUAWLFAoFS5csom2r5sTExODSohWTps5I0Rh+vr4cO3IYgKbNW6kjTLXIFr9C+eGdetpSpFUZxwoA3L5+OZ0jEQRB+D+R/AmCkCJr1qxBoVD88KhSpUp6h6YSUpmMNiNmoWtoxD3v6yyfP00j81pmzcaEuSuQSCRs27iGHZvXaWTe5CpRuixzvdYilUrZtH410yaOSdU4UqmUWQu8EhLAHl06sHHdGtUGG8/UzIy1m7Yzc+5CdHV1OXn8GGVLFmHXjm1J3quvr0//QUO49/gF4yZOwcLSktc+PngOGUhuh+z079uLO3duqyXu5AoMDMStQzsGePQhLi6O9h3cWLZq7Xe9dZNj5fKlxMTEUKpM2WS3hUiL2DjlNlppCuP8r6zZrAH4HPCJqKioNMelaiVKl0MikfDG5wUB/n7pHY4gCAIgkj9BEIQfmGXJRvOBkwBYs2QWNy6f08i8ZSpUoZvHcADGDPXg/l1vjcybXDXrNGD8NGXT97kzp7J8yYJUjfMtAXR164pCoaCPexdWLluiylATSCQSOnXtwakL1yhStDiBnz/TsV1rXNu0wM/XN8n7jYyMEpLAeQuXkDdffkJDQ1m2dAmOpYtT0bE0ixbM02iV65iYGNauWUXxIvnZvnUzMpmMiVOms9BreUIbheQKDQ1lmdciALq791FHuD+IjD/rp6urm6ZxzM0zJSS6nwMyVq8/AGMTU3LlyQ/A3ZtX0zkaQRAEJZH8CYIg/ESxavUoU7c5CoWC0QO6aaT9A4Bbz4FUqOpMZGQEvdxap6kXmjq0cu3MAE/lqt8oz4Fs3ZS6FUqpVMq0OQvp1rMvAIP792HuTPWtsubNl59jpy8weNhI5HI5e3btpHTxQmxctyZZW1j19PRw69KNq7fusu/QMRo3bYaWlha3bt5gyKD+5HbITs1qTsyZNYOHDx+opVpsUFAQy7wWU7JoQXp278InPz/y5M3H0X/O0rf/QCQSSYrHXDR/LgH+/uTImYtGTV1UHvPPhIaGAKBvYJCmcaRSKWbmmYC09QxUp+KllG0z7t/+ddEhQRAETRHJnyAIQiIa9x2NhW0OPvl+YPzQnhpp/yCVShk3aynWtva8feNDf3e3DFdt0t1jCB279QZgQO/uHNq/J1XjSCQSxk2eQf/BwwAYP2YEo4cPUdv3WVtbm2Ejx3LizCUKFylG4OfPuHfrTH3nGjx6mLw+hhKJhCrVqrNu0zYev3jDjDnzKVPOEYVCwcUL5xk5fCilihUidw4bOrRvw5JFC7h29Qrh4eEpjlehUODz6hXr1q6mTUsXctplo3+/3jx79hTzTJmYPG0mF6/dokzZcikeG+DN69fMiU+4h40al+JVw9RQKBQExbffMDExTfN4ZmZmAHwJDEzzWOpQtERpAO55/xlnogVB+P1JFJp4N5NGwcHBmJiYEBQUlCFLxAuCkDLffqcnHfJG18AovcP5pffPHjLPvSkxUVF4jJhEm069NDLv00f36OxSi4iv4XTrPZAhoyZoZN7kiouLY3h/d3ZsWY+WlhZrt+yiWg3nVI+3ZMEcxo0cCkDrtq7MXbQULS0tVYX7g+joaJYsmMu0yeP5+vUrcrkc9959GTJsJCYmJike7+2bNxw8sI8jhw5w4dzZH9oYSCQS7OzsyZEzFza2NmTNaoWpqRkGBgbItbSIjYkhPDycwMDPfPjwnpcvXvDgwX38P32/nTFvvvx06tqd9h3cMDQ0TPXrVygUNG1Yl5PHj+FYoSIHjp5K1cphSn0JDCRHdgsAXvkGp3nrZ93qFbl5/SpL1mylZp0GqghRpR7cu03D6o4YGhlz4uYrpFL1feYeGhJMtWK24r2SIPwh1JX/iORPEASN+52SP4ALuzewa+4YZHItVmw7QsGiJTUy77H9Oxnp0RmAuV5rqd+kuUbmTa6YmBj6u3fk8L5d6OjqsnHbXipWrprq8bZsXMfAPt2JjY2lRq3arFq/JU0JTnK89nnFsMH9OXxwP6BsFj9y9Djad+yU6pWwr1+/cu3KZS5eOM+1q5fxvnWTT36pK/ghl8spXrIUVavVoH7DRhQtVlwlSdrCeXMYPnQQurq6nLpwjbz58qd5zOR4+OA+FUoXxdTUjEc+SZ+5TErzhrU5d+YfZi9eTcNmLVUQoWpFR0dTNKclUZGR7PrnFtntHNQ2l0j+BOHPoq78R/17PARBEH5z5Ru35dmtS9w5c4ThfTqyfv85jFWwZS0ptRo04/GDO6xfNo+hHj2wz5mLQkWKq33e5JLL5cxatIrIiAj+OXaI9i2bsHnXAcqVr5iq8Vq1dcU8Uya6d2zDiWNHaOBcjS0795Ela1YVR/5/tnb2bNy2m+NHDjHCcxDPnj6hX293Fi+cz5jxE6nXoFGKky09PT2cqlTFqcr/E2E/X1+ePnnMq5cvePv2LX5+vnwJDCQ8PIyYmBikUil6+vqYmZmTJUtW7OztyZM3HwULFU7z6th/nTp5glHDlausE6bM0FjiB/D2tQ8A1jY2KhlPJ/57ExGRcXpj/puWlhZ58xfkrvdNHj+4o9bkTxAEITlE8icIgpAEiURCiyFTeff0AR/evWb8kJ7M8NqokW1yPQeN5tmj+1w6ewL3ji3ZfeQcmS2zqH3e5NLW1mbBio306NCcc6dO0NalIZt27qdsfI+zlKpVux47DxynXYvG3Pa+Sc0q5dmycx8FChZSceTfq1m7LpWr1WDVci9mTJ3I40cPadOiGSVKlWb4qDHUrFU7TT9vyyxZsMyShQqVnFQYdcrdvHGdtq1ciI2NpUWrtnTq2kOj87948RwAOxUlQdrxW4NjYtTfjzO18hUozF3vmzx9eJfqdRqldziCIPzlRMEXQRCEZNAzNMJ13AJkWtqcPXGIjSsWamRemUzGxHkrsHXIxYd3b3F3a0VkZKRG5k4uHR0dlqzeSgWnaoSFhdKmWQOuXLqQ6vFKlCrDweNnyZEzF2/fvKZODSdOHj+qwoh/Tltbmx69+nLz7hMGDPZEX1+fm9ev4dKoPlUrObJ/727i4uLUHoe6XLl0kYZ1axEaEkJFp8rMW7xMIx9g/NvjRw8ByJUnr0rGk8SfocvIP5d8BQoD8Oxx8ooKCYIgqJNI/gRBEJIpe55CNO4zCoCFM8Zy69pFjcxrZGzKrOVbMDI24db1K4wY2EsjlUdTQldPD6+12yhfqSphYaG0blqfi+fPpno8h5y5OHDiHOUqVCIkOJiWTRuwbMlCjbxuE1NTRo6dyK37z+jZxwM9PT1uXr9G25YulC5WiNUrlqWqemd62rFtCw3q1CQ4KIhy5SuwcdsedHR0NB7H/Xt3AMinombyivikT9NJbErkyVcAgBdPHqZzJIIgCCL5EwRBSBHHhq0pUbMRcbGxjOjbCf9PaS9akRx2DrmYsnAtMpmMPds3sWTeDI3MmxJ6+vosW7+DCpWrEx4eRhuXBpw9dTLV45mbZ2LbnsO0bOtKXFwcnoM88OjdQ2MrnxaWlkycOhPvB8/pP2goxiYmPH3ymH693cmX05YRnoN5+vSJRmJJrbCwMPr37UUn17ZERETgXKce2/ccwshI84WWoqOjuXfnNgCFi6rm7GpMbAwAMlnGPcWSK28+AN6/9SEyMiKJqwVBENRLJH+CIAgpIJFIcBk4kawOufH3+8iIvm7ERGvmvFGZClUYOGY6ALOnjOXQvl0amTcldPX0WLZuO1VqOBPx9SvtWjbm2JGDqR5PW1ubuYuWM2biNKRSKevXrKRhnep8+PBehVH/moWlJaPGTeLu41dMmjYLO3sHvgQGsmDubEoWzk+dGlXZsHY1wcHBGospKQqFgsOHDuBYsigrl3kB0H/QUDZs3YVBGpurp9bdO958/foVExNTcubKo5IxIyOUHwToqLgojipltsiCkbEJcXFxvHn1PL3DEQThLyeSP0EQhBTS0dOnw/jF6OgbcuvqRRZMH6OxuV3adqZVR2WRjsG9u3Dr+lWNzZ1cOrq6LFq1hVp1GxIVGUmnts3Zs3NbqseTSCS49+nPhu17MTEx5dqVy1SrUIbLF8+rMOqkGRkZ4d67H9fvPGLzjj3UdK6DVCrlwvmz9OzehVy2VrRr5cKObVvSLRFUKBScO3OaBrVr0rJpI169eol1dht27jvMqHGTkMlk6RIXwPmzZwAoXa68yvrdhYeHAaRbQpscEokEhxy5AETyJwhCuhPJnyAIQipY2uag1TDlKtzmVYs5tn+nxubuN3wSlarXJjIygm7tXfB59UJjcyeXjo4O85atp2HTlsTExODeuT3rV69I05jVajhz5NRF8hUoiK/vRxrUrs7iBXM1fv5RJpPhXKc+W3ft5/ajF4wcO4HcefISERHBvj276eTaFgdrSxrWqcWCubO5e+e22guSBAQEsHK5F06OpannXJ2zZ06hra1NH4+BXLx+h6rVa6p1/uQ4dfI4AE5VqqlszODgIAAMDTN2Xzv7hOTvZTpHIgjC304kf4IgCKlUxMmZam2Vq3DjPXvz9NE9jcwrk8mYMGcF+QoWJfCzP13aNCHwc4BG5k4JLS0tZi5aSZsOXVAoFAz26Mm8mVPTlKw55MzFwRPnadysBbGxsYz0HESHti0I+vJFdYGngLV1dgYMHsblm/c4feEaHgOHkCt3HqKjozl96iQjPAdToUwJ7K0tadG0IdMmT+TY0cO8f/cuTd+HyMhIrl29wrzZM2lYpxa57bLRv08vbnvfQldXl05de3D9ziPGTZqWLuf7/is4ODihAFC1ms4qG/dzgPLPvYmZmcrGVAcbO3sA3r15la5xCIIgSBQZrWTcT6irw70gCOnj2+/0pEPe6Bqk/xvTtIiLjWX50M48uXaObDZ2rNl9ClMzc43M/cn3A52a1cT3w1tKlnFk7bYD6OrpaWTulFAoFMyeMjahSE1X9z6MmzwjTVv/FAoFq5YvYezwwURHR2Nn78DyNRsoVbqsqsJOk2dPn3DsyCFO/3OCSxfOERYW9sM1JiYm5MiVGzs7O6yyWWNpmQVTM1MMDAzR1tZGIpEQHR3N1/BwAgMD+fjxA2/fvObZ06c8ffKY6P+cNS1UuCgt27SjdVtXzDNl0tRLTZZtmzfSo0sHcufJy7lrd1UyZlxcHDaZDYiNjeW891OyWlmrZFx12L5pLcP6u1OuUnXmr1HPLoHQkGCqFbMV75UE4Q+hrvxHJH+CIGjcn5T8AYQHf2FOt8Z8/vCGMhWqMHfVDuRyzVQffP7kIV1bOBMaEoxzvUbMX74hXc91/crqpQuZNHoIAI2aNme+16o0txu4deM63d3a8trnJXK5nBGjx9On/yCVnSlThejoaO7cvsW1K5e5ef0at2/f4sWzp8TGxqZpXPNMmShT1hGnKtWo6VyHnLlyqyhi1WveuB4njx9lwNARDBmumjOyfr4fKZLHFqlUyoM3XzT2O5caF878Q4cW9XHIlZetR6+oZQ6R/AnCn0UkfyL5E4Q/xp+W/AG8f/6IBT1diIr4SutOPek/YrLG5r555Tx9OjYlOiqKtm7dGDtlTobte7Zv51aG9utGdHQ0jhWdWL1hO6Zp3LIXHBTEoH7u7Nu9A4BKTlVYvGIN1tbZVRGyWkRERPDi+TNevnjOm9c+fPzwnk+fPhEc9IXQ0FCio6NQKBRoybXQ09fH1NQMC0tLstvY4pAjJ/nyFyC7jW2G/Tn/29u3byiWPydxcXFcvHmfHDlVk6TevH6VutUrksUqGxe8n6lkTHV58ewJtSoUw8DQiFO336hlDpH8CcKfRV35T8b9mEwQBOE3ki1nPloPn8na0b3YvGoxufMVon6zNhqZu0TZioyduZSR/TqxcfUyLC2z0muAp0bmTqmGzVqSKbMFPTu15tL5szRwrszG7fuwjT8TlRrGJiYsXb2RKtVqMmJof86dPU3F0sWYOXchTZu3zJAJkq6uLgUKFqJAwULpHYrarVmxlLi4OMpXqqyyxA9IKHRka+egsjHVxTKrFQBhoSGEh4Wib2CYzhEJgvC3yjj7YgRBEH5zRSrXpmaHPgBMGuHBnZuaa8NQs14TBoyaCsCcaePZsm6lxuZOqQqVq7Fl33GyWGXj6eNH1KlWkZs3rqVpTIlEQhtXN06ev0bxkqUJCvpCV7d2dHJtjf+nTyqKXEipsLAw1qxaDkCnru4qHfvZ0ycA2DnkVOm46mBoaISenj4A/n6+6RyNIAh/M5H8CYIgqFCtjn0pXKkWsdFReHRrzcf36tni9TMtO3Sno/tAAEYP7ceRA3s0NndK5S9YhB2HTpO/YGEC/P1oUrd6wrbNtMiRMzf7jp5m0LBRyOVy9u7agWOpIuzZtUPjLSEEWL1iKZ8DArB3yEmd+o1UOvaTRw8ByJU3v0rHVZfMFpYAfPnsn86RCILwNxPJnyAIggpJpVJaD59Jtlz5CQ0MYGC31oSHhWpsfveBI2ncsgNxcXH0d+/I+TMnNTZ3Sllly87mfSeoWqM2kRERdOvYhlnTJqY5SdPS0mKQ5ygOnjhPvgIFCfD/RKf2rXBt7cL79+9UFL2QlODgYObNVvbC7DtwqMoLEd2/exuAfAV+j62z5pkyAxAokj9BENKRSP4EQRBUTEffALdJSzE0y8TTh/cYPaBrmis7JpdEImHohNlUq9OI6KgoenRoyc1r6qkuqAqGhkZ4rduOW3fldtkZk8fTrWObn7ZGSKmixUtw9PRl+g8Zjlwu5+D+vTiWLMyq5V4a+3n8zWZNm0SAvz+5cuehRet2Kh076MsXXjxXFnkpUKioSsdWl2+9CEOCvqRvIIIg/NVE8icIgqAG5lmtcZvohVxbm7MnDrNwmmrK2yeHTCZj/KxllK1UjYiv4XRu05gH925rbP6UkslkjBg/jUmzFqGlpcX+PTtp6FyZ1z6v0jy2jo4OQ0eM5diZyxQvWZqQ4GAGefTGuVpFbt+6mfbghZ969PABXovmAzB64jSVt2G4FX9G1MbOIWFFLaMzNjYFICQkKH0DEQThryaSP0EQBDWxL1SCVp7KbW8bVy5k9+Y1GptbW0eH6YvXU7RkOUKCg+jQvAHPnz7W2Pyp0bKdG+t3HiZTZkvu372DcxVHzp5SzbbVAoWKcOD4WSZOn4OhkRE3r1+julM5Bnn05nNAgErmEJRiYmLo496F6OhoatWpR63a9VQ+x+WL5wAoUbqcysdWF0MjZVubsNCQdI5EEIS/mUj+BEEQ1Kh49QbU7uQBwLQxA7l0VnNn8PT0DZizciv5ChYl8LM/ri51E8rjZ1SlypZn97HzFC5WgsDPAbRqWo8Fc2aopFiLTCajS/deXLh+jyYuLYmLi2PVci9KF83Pcq9FREdHq+AVCLOmT+bGtasYm5gwddYCtcxx/uxpAMpVcFLL+Orwrb1DuAq2NAuCIKSWSP4EQRDUrIZrb0o5NyEuNpYhvTrw9NE9jc1taGTC/DW7yJE7P74fP9C+WR3evXmtsflTI5t1drbsPYFLq/bExcUxaewI3Nq6EPTli0rGz5LViiUr17PzwHHyFyxEYOBnhg7sR8WyxTlyaL+oCpoGp/85wYwpEwGYMnMe2ayzq3yOwM+fuXld2UalglM1lY+vLrq6ugBERnxN50gEQfibieRPEARBzSQSCc0HTSJnsbJEhofSv3NLfD9oruqkqXkmFq7fg61DLt6/fUO7prV5/+6txuZPDR1dXabM9WLijAVoaWtz5OB+alUup9JzehUqVeb42atMnbUA80yZefr4EW2aN6FB7Wpcu3pZZfP8LZ4/e0qn9q2Ji4ujTXs3mrVoo5Z5Tp08SlxcHLnzFiBbdhu1zKEOOjrK5C8qMjKdIxEE4W8mkj9BEJLt1atXdO7cGQcHB/T09MiZMydjxowhKioqvUPL8OTaOnScuIQsdrnw+/iO/l1aEKrBwg+ZLbKweMM+sts68Ob1K9o3q8NHDSagqSGRSGjl2plt+0+S3cYOn1cvqF/LiZXLFqtsdU4ul9OxS3cu33pIb49B6OrqcvH8OZyrVqRtiybcu5NxC+VkJB8/fKBFk/p8+RJIiVJlmDxzntrmOrh3NwA11HCWUJ3kWloAxMSI7cWCIKQfkfwJgpBsjx49Ii4ujqVLl3L//n3mzJmDl5cXw4cPT+/Qfgv6RiZ0mbYSI/PMPHt0n6E9XYnWYOJsmTUbizfuwyq7LT4vn9O2Se0MnwACFC5Wkr0nLlKjdn2io6IYMdiDzu1aEPj5s8rmMDYxYeS4yVy4cZ/W7ToilUo5fHA/To4l6dC2hUgCf+GTnx9NG9Tm5Yvn2No5sHbzzoQtjqoWHBTE8WOHAajTsKla5lCXb30O4+JEmxFBENKPSP4EQUi22rVrs3r1amrVqkWOHDlo2LAhgwYNYteuXekd2m/D3Co7XaatREfPgGsXzzDBszdxcXEamz9rNhu8Nh34LgH88D5jbwEFMDE1Y8marYycMAMtLS0OHdhL9YqluHj+rErnsc5uw5xFyzh79TaNmjZHIpGwf88unBxL0qZ5Y7Ed9D/evnlNfeeqPHp4n6xW2di+9zAWllnUNt/+PTuJiowkZ5585C9YRG3zCIIg/KlE8icIQpoEBQVhbm6e3mH8VrLnKYTr+IVIZXKO7N2m0R6AAFbWtj8kgO/fvtFoDKkhkUjo2K0X2w+dxj5HLt6/e0uz+jWZPG6kyrce58qdl6WrN3Lq0s2EJPDIoQM4V61IfeeqHD64X6NJe0bkfesGtapU4OmTx1hnt2HXwePYOeRQ65wb160CoFnLdkgkErXOpWrftipLJOKtlyAI6Uf8DSQIQqo9e/aMBQsW0L17919eFxkZSXBw8HePv12+Mk60HDIFgA0rFrBx5UKNzv8tAcxmY8frVy9o07gWb1TQVF0TChUpzt4TF3Fp7YpCoWD+7OnUr1GJx48eqHyufPkLsnT1Rs5du0Ordh3Q0tLi4vlztG3RhLLFC7JsycK/7s+zQqFgw9rV1K1RmY8fP5A3fwH2HT1Njpy51Tqv980b3Lx+FS0tLZq2aKvWudQhJiYGAJmKG94LgiCkhEj+BEHA09MTiUTyy8ejR4++u+fdu3fUrl2b5s2b07Vr11+OP2XKFExMTBIeNja/T4U+dSpVuyn1ug8BYN7kkRzes1Wj81tZ27J000Fs7HPy9o0PrRvX5OXzpxqNIbUMDAyZOteLhSs3YWpmzp3bt6jpVJYlC+YQG6v6M1W5cudl7qLlXL3zhF79BmJsYsLzZ0/xHORBwdy2DOzXi7u3vVU+b0YT+PkzXTu2o2/PrkRERFDDuS77j57BWgNVN5ctVhaRqdOwGZnVuLVUXaKilFU+tbS00zkSQRD+ZhLFb9DQKDg4GBMTE4KCgjA2Nk7vcAThj/Pp0ycCAgJ+eU2OHDnQ1la+aXn//j1VqlShXLlyrFmzBqn0158jRUZGEvmv8ubBwcHY2Ngw6ZA3ugZGaX8BvzGFQsG+RZM4u301UpmcWUs3UaFqLY3G8Mn3A71dG/Py2WMsLLOwdtsB8uQvqNEY0sL343uGD+jJmZPHAChTrjxzFy9X60pUWGgoWzevZ/WyxTx98jjh+WLFS9KmfQeaNW+F2R+0HVqhULBj62ZGeg7i0yc/ZDIZQ4aPoc+AIUn+/qvCqxfPKV+yIHFxcew9cZGChYupfU5Vmz5hJMsWzqZ1p570HzFZ5eOHhgRTrZiteK8kCH8IdeU/YuVPEAQsLCzIly/fLx/fEr93795RpUoVSpYsyerVq5P1xk9HRwdjY+PvHgDepw6p9XX9DiQSCQ16DqdEzUbExcYwpJcr3tcvaTQGiyxWLNl4gFz5CvLJz5dWjWtx1/uGRmNIiyxZs7Fi424mzlyIgYEhVy9fpGr5kmpbBQQwMDSkU1d3zl69w459R2nYxAUtLS28b91gyIC+5MthTftWzdi9czvh4eFqiUFTLl+6QJ0aTnTv7MqnT37kzpuPA8fP0W+Qp0YSP4DZMyYTFxdH5eq1fsvEDyA8PAwAPT39dI5EEIS/mUj+BEFItm+Jn62tLTNnzuTTp098/PiRjx8/pmq87bPH8v75o6Qv/MNJpVJaeU4jf7kqREdG0LdzC548uKPRGMwzW7Bk4wEKFi1J8JdA2jWry9VL5zUaQ1pIJBJate/EoTPXqVC5OpEREYwbOZS61Sty/6762jRIJBIqVq7KsjWbuPXoFeOnzKRg4SJER0dzcP9eOru2JrddVjq0bcGOrZv5EhiotlhUSaFQcPqfEzSp70zdGpW5evkSevr6eI4cx4lz1yhespTGYnl4/y47tmwEoO+gERqbV9VCQ0IAMDAUq3KCIKQfkfwJgpBsx48f59mzZ5w8eZLs2bNjZWWV8EiV2CjWjHQnPPiLSuP8HcnkWriOW4hD4VJEhIbQw7UJPi+faTQGE1MzFq7bQ8myFQkLDcGtZUNOHT+s0RjSytrGljVb9zF59mKMjE24fesGzlUcmThmuNpX4DJntqBbz76cPH+dU5du0qf/YGztHPgaHs7+Pbvo1qk9ue2yUt+5KnNmTMX71g21rUym1ic/P7wWzad86aI0bVCbM6dOIpfLadehM5duPsBj8DB0dHQ0Fo9CoWDsiKHExcXhXL8xRUuU1tjcqhb0RZn4GxmbpHMkgiD8zcSZP0EQNO7b77SWiSXRQX7kK+NE56krkMY3Qf6bfQ0NYYlHW949vU8Wq+ws23oIK2tbjcYQEfGV4X06cv6fo8hkMqbNX0Zjl9YajUEV/Hw/MG74QI4e2AOAja09k2fOpaZzXY3FoFAouON9i0P7d3Pk0H4eP/y+IqmpmRnlK1SirGMFypRzpGixEmprkJ4Yn1cvOXHsCAf37+XcmVMJCam+gQGt2nagR28PbO3sNRrTN/t276BbxzZoaWtz5NxN7OzV20pCnZrXq8qt61eYtngdVZ0bqnx8ceZPEP4s6sp/RPInCILGffudzuk2hxfrPVHERFK9nTt1uw5K79AyhJBAfxb1bc2n1y+wscvB0i2HyGyZVaMxxERHM8GzF4f3bANgxPjpuHXvrdEYVOXk0YOMHdafD++Uzeyd69Zn/JRZ2Nk7aDwWn1cv+ef4UU7/c4wL584kbAX8Ri6Xky9/QQoXKUr+goXImy8/ufPkJbuNLXIVtAgIDg7m0cP73PG+xc3r17h86QKvXr747pqixUvSsq0rLi3aYGySfqtUgZ8/U7lcMfx8P9J74DA8hoxKt1hUoVrZQrx+9YKlWw5RvHR5lY8vkj9B+LOI5E8kf4Lwx/j2O13Icy/BTy7zepey353ruIUUrVInnaPLGL74fWBRn1Z8/viWHLnz47XpAKbmmTQaQ1xcHHMnj2DL6iUAdOs9kMEjx/92zbUBwsJCWTR7Kqu85hMTE4O2jg69+g2kt8dgDAwM0iWmmJgY7njf5NKFc1y7cpHrV6/g/8nvp9fK5XKyWWfHOnt2slplI3NmC0xMTTE2NkFfXx9tbR2kUilxcXHExEQTHh5OSEgwgZ8/4+v7kffv3vL61St8fX88nyuTyShVphw1nOtSr2FjtffrS64endqxZ+c2cubOy74Tl9DR8IqoKikUCormsCQ8PIwdJ25g65BT5XOI5E8Q/iwi+RPJnyD8Mf6d/Ml0DHh/bCmfLm1HqqVL/6U7yZYzX3qHmCEEvH/Nwj6tCPb3JW/BIixavw9jE1ONxqBQKFjrNYfFM8cD0KRFWybPXoyWlpZG41CVp48fMn74QC6dPw1ANuvsjBg7kSYurTRWuTIxCoWCd2/fcPf2Le7fu8OjB/d5+uQRr148/65VSlplyWpFwcJFKVq8BKXLOlK6jCNGGezf1q2b1tHPvQsymYxtB/75rc/6AYQEB1E8t/Js9Jm779DTV/0HDiL5E4Q/i0j+RPInCH+M/yZ/irhYXmwcRuiLm5hb2eCxdDcGJmbpHWaG4OvznMX9WhMaGEDBoiVZsHY3hkaa/3tw/44NTB7ej9jYWCpWqcHClRsxNPw9ezQqFAqOHtzLlLGevHvzGoBiJUoxdtJ0ypWvmM7R/Sg2Nhbfjx9489qHD+/e4ufnS4D/J758+UJoSDBfw8OJio4mNjYWqVSKtrYWurp6GBkZY2pmhoVlFrJaZcPG1h6HHDkxMTVN75f0S/fv3qZeTScivn5lgOcYevYfmt4hpdnjB/eoV7UMxqZmnLjxUi1ziORPEP4sIvkTyZ8g/DH+m/wBxIQH8XRFb6ICP5CrhCPdZqxGJv89V5dU7cPzxyzu35bwoECKlCjLvNU7MEiHxOvCqWMM69ORiK/h5C9UhBUbd5ElazaNx6EqkRERrFq6AK95MwgLCwWU5wGHjZ5Avt+oyf2f5NMnP+pUq8Db1z5UqlqDlZv2pPuKrCqcOHKAHh1akK9gUdbtO6OWOUTyJwh/FtHkXRCEP5pc3wT7VuORauny7OYl9i6clN4hZRhWOfPSfeZa9AyNuXPzCv27tCA8PlnRpApVa+G16QDmmSx4eO8OLnWr8PjBPY3HoSo6urq49xvMyct3ae3aGZlMxtFDB6jqWII+PTrh80o9KzTCz4WFhuLasglvX/tg55CTOUvW/BGJH4DPK2VRHWs7zRcZEgRB+Lc/429VQRD+CHqWDtg2HQbAhd3rubx/SzpHlHFkz1OQbjPXomtohPe1Swzo2pKv4WEaj6NAkRKs3Hkcuxy5+fDuLS0a1OD8mZMaj0OVMltmYcKMBRw6cx3neo1QKBRs37yBCiULMsSjF+/evknvEP94ERERuLVtzq0b1zA1M2fFxl2Ympmnd1gq8+r5UwBs7XOlcySCIPztRPInCEKGYpKvAlmrdgRg++zRPPe+kr4BZSC2+YvQfeZadA0MuXnlAv27tEiXBNDaxp4V249RvEx5wkKD6dy6MZvXrdB4HKqWM3deFq3azK4jZ6lQuToxMTGsW72ccsXyMcSjF699XqV3iH+k8PBw3No25+zpk+jrG7B8wy4cMkjFUVV59uQRAPZ/2OsSBOH3I5I/QRAyHMtKbTEtWAXiYlnq2YOA96/TO6QMwzZ/UbrNWJOQAHp0bp4uW0BNTM1YsGY3dRq3IDY2llGD+zJp9NCEBuG/syLFS7F223427z1OuQqViY6OZt3q5ZQvUYA+PTrx+NGDpAcRkiXoyxfauDTg1Imj6Onps2zDToqXKpPeYamUQqHg8cP7AOTMkz+doxEE4W8nkj9BEDIciUSCTaNB6GXLQ+zXYFYO68bX0JCkb/xL2BUsrtwCamDIrasX6efmQmhIsMbj0NbRYezMpXTvPwKA1UsX0N3VhZB0iEUdSperwIZdh9m051jCSuD2zRuoXLYYrq2acPnieX6DmmkZls+rlzRwrszlC+cwNDJm9dZ9lKvglN5hqdy7N68JDvqCTC7HPmfe9A5HEIS/nEj+BEHIkKRauji0HI/cKBO+r56yYVxfYmNi0jusDMOuQDG6z1qHrqERt29cpq9bM0KCv2g8DolEQufeg5k0fzU6OrqcPnGU5vWqJhS4+BOUcazI2m372Xn4DLXqNkQikXDs8EEa16mGcxVHdmzdSFRUVHqH+Vs5ffI4zlUcefLoIVmyWrF57zFKlS2f3mGpxf27twDlqp+2jk46RyMIwt9OJH+CIGRYWsaZcWg1AYlch0dXz7JvkagA+m+2+YvSY/Z69IxMuHfrGr3aNyboS2C6xFKzXhOWbjmMRRYrnj1+SBPnSlw8eypdYlGXoiVKs3j1Fo6ev0Wr9p3Q0dXljvdNendzo2TBnEybNFYUh0lCdHQ0U8aPonWz+nwJ/EyRYiXZeeQs+QsWSe/Q1Ob2zRsAFChcIp0jEQRBEMmfIAgZnH62PNg29QTg/K51nN+9Pp0jylhs8ham59yNGJiY8+ieN+5t6/PZ/1O6xFKgSHHW7P6HgkVLEvwlELdWDVm9dOEftzUyR648TJy5kLM3HtN/6GiyZLXik58vc6ZPpnTh3Li2asKxwweIESvV37l3x5u61Sowb9Y0FAoFrdp3YvPe42S1sk7v0NTq1vXLABQqXiqdIxEEQRDJnyAIvwHT/JXIWq0TALvnjefh5dPpG1AGky1XfnrO24iRuQXPHt2ne+u6+H54ly6xWGSxwmvzQeo2aUVsbCyTRg9hcJ+uRHz9mi7xqFOmzBb0GuDJ6euPmLdsPWXKVyIuLo5jhw/i2qopJQvmZMLoYTyKL/bxtwoJDmbcSE+cqzhy9443pmbmzF++gYkzF6Kjq5ve4alVZEQEt29eB6BoKcd0jkYQBEEkf4Ig/CYsK7bGrJgzKOJYNao3758/Su+QMpSsDnnotWAzppZW+Lx4SvfWdXn3+lW6xKKjo8uYGUvoP3IyMpmMPds30aJBNd6+9kmXeNRNS0uLeo2asWn3UY6ev0WnHn0xy5QZ348fWDRvFlXKFadmpTIsmjeLt2/+nsq1UVFRrF7uhWOJAixZMJvY2Fic6zfm8Nnr1G3YNL3D04hbN64SFRVJJoss2NrnTO9wBEEQRPInCMLvQSKRkL2+B4b2xYiL+sqKoZ0J8vdN77AyFIvsDvRasJVM1ra8f+ND15a1ef7kYbrEIpFIaO3WkwVrd2NqnokHd2/TsGZ5zp46ni7xaErO3HkZPm4qF7yfsXj1Zqo710Mul3P3jjcTRg+jVKFc1K1ekcXzZ/PqxfP0Dlctvn79ypoVSylfsiDDBvXF/5MfDjlzs3LTbhat3ISFZdb0DlFjLpw5CUApRyckEkk6RyMIgpDK5G/RokXY29ujq6tL2bJluXr1aqLXLl++nEqVKmFmZoaZmRk1atT45fWCIAiJkcq0sGsxBp3MtgR9+shKz65EpkOT84zMPKs1vRdsJatDHvz9PtK5ZR0e3LmZbvGUcnRi3d7T5C9cnOAvgXRu3ZgFsyYTFxeXbjFpgra2NrXqNmLpuu1cuvuS8dPnUdqxIhKJhJvXrzJ+lCfliufHqWxRJo4ZzsXzZ4mOjk7vsNPktc8rpowfRcmCOfEc2Ie3r32wsMzCmCmzOXTmOpWrO6d3iBp37vQJAMpWrJrOkQiCIChJFCk8ib9161ZcXV3x8vKibNmyzJ07l+3bt/P48WMsLS1/uL5t27ZUqFCB8uXLo6ury7Rp09i9ezf379/H2jp5h7yDg4MxMTEhKCgIY2PjlIQrCEIG9O13upDnXmQ6Bim+PzLwA89W9CEm/Av5y1XBbdJSZHK5GiL9fYUHf2H5kE68fngbHT0DZi/bROnyldMtnsjICGaP92T3ljUAVKpag1mLVmGeKXO6xZQe/Hw/cPTgXo4d3MfVS+eIjY1N+JqhkREVKlWmUuVqlK/oRL4ChZBKM/YGncDPnzlyaD+7tm3m/NlTCcV9rG1s6dyjHy3adkRXTy+do0wffr4fKF9EudXz8JUnZMr843skVQoNCaZaMVvxXkkQ/hDqyn9SnPyVLVuW0qVLs3DhQgDi4uKwsbGhT58+eHp6Jnl/bGwsZmZmLFy4EFdX12TNKZI/QfizpDX5Awh7+5DnawehiInEsWFrmg2YILZV/UdEeChrRrrz9MZFZFraTJq7nGq1G6VrTAd2bmLa6IFERnwlazZr5i9bT4nS5dI1pvQS9CWQs/8c59SJI5w7fYLAAP/vvm5qakapso6UKl2W4iVLU7R4SUzNzNIpWqW4uDgePbjHmVMnOXnsCJcunP0uga3gVI3WHbpQo3Z95H/5BzKb161g1OC+FCxaktW7Tqp9PpH8CcKfRV35T4r+Zo6KiuLGjRsMGzYs4TmpVEqNGjW4dOlSssYIDw8nOjoac3PzRK+JjIwkMjIy4f+Dg4NTEqYgCH8Bg+z5sWs6jFfbxnFp32bMslhTvZ17eoeVoejqG9Jl6go2ThzAnTNHGNbHDc/xs2nSumO6xVS/WRvyFSqKZ68OvH75jNaNajJw+Di69PTI8KtcqmZiakaDpi1o0LQFcXFxPLjrzYWzp7h0/gw3rlzky5dAThw9xImjhxLusbVzoGDhwuTLX5A8+fKTM1decuTMhaGRkcrji4uL4+2b1zx6cI+7d7y5deM6N65eJjDw83fX5c1fiLoNm9LIpTXZbe1UHsfv6siBvQBUqVU/nSMRBEH4vxSt/L1//x5ra2suXryIo+P/SxYPGTKEM2fOcOXKlSTH6NmzJ0ePHuX+/fvoJlLieezYsYwbN+6H58WnWYLwZ1DFyt83n67s5v2RRQC0GTGLkrUaqyDCP0tcbCw7Z4/i8oGtAHTt50mXPkPTdaU0LDSEKSM8OHZgJwBO1WoyY8EKMmW2SLeYMpLo6Gge3rvNjauX8b5xlTveN3jj8zLR683NM5HdxhYra2uyZLEis6Ul5pkyY2JigqGhEXp6+ujo6iasxsXFxREdFUX413BCQ4IJ+hJEQF3bCToAADsFSURBVMAn/Hx9+fD+LW9e++Dz8gVff9KiQ1/fgFLlylOpSk2q1qqDvYOoYvlfAZ/8KF80J7Gxsez65xbZ7RzUPqdY+ROEP0uGWPlLq6lTp7JlyxZOnz6daOIHMGzYMAYMGJDw/8HBwdjY2GgiREEQfjMWZZsQHeTHp0vb2TxlKEbmFuQpVSG9w8pQpDIZLoMmYWRuwfF1C1k+byr+fr4MHjsj3bbmGRgaMWHuCkqWq8TsCZ6c/ec49auWYdaiVZR3EsUxtLS0KFK8FEX+1Rj8S+BnHt6/y+MH93jy6D7Pnz7mxfOnBAb48/lzAJ8/B3Dn9i2Vx5EjV17yFSxM4aIlKF6qDAUKF0NLS0ul8/xpDuzZQWxsLAWKlNBI4icIgpBcKfpXP3PmzMhkMnx9vy+v7uvrS9asvy7dPHPmTKZOncqJEycoUqTIL6/V0dFBR0cnJaEJgvAXs6rZlegQf77cO8XyYT3ot2gL2fMUTO+wMhSJRELtzv0xMrdg97yx7N68moBPH5k4dyW6evrpFlOT1h0pUqIMw/t14uXTR3RoUZ+uvfrjMXQ02tra6RJXRmVqZo5jxco4Vvy+cE9ISDBvX7/i/ds3+H58j5/vRz77fyIw8DPBQUGEhYYQGfGVyMhIYmJiAOWRDS0tbXT1dDEwMMLE1BRTM3MsLLOQxSob2bLbYmefg+y29n/92b3U2Ll1PQB1GrdM50gEQRC+l6qCL2XKlGHBggWAcuuIra0tvXv3TrTgy/Tp05k0aRJHjx6lXLmUH+wXBV8E4c+iym2f38TFRPFi4zDCXt3GyNyCPou3k8lK7Bj4mTtnj7JxggcxUVEUKl6aWUs3Y5bOVTcjvoYzZ+LwhGqghYoWZ/bi1eTIlSdd4xKElLp35xaNa1ZAS1ubgxcfYWqWeI0DVRLbPgXhz6Ku/CfFp+sHDBjA8uXLWbt2LQ8fPsTd3Z2wsDDc3NwAcHV1/a4gzLRp0xg1ahSrVq3C3t6ejx8/8vHjR0JDQ1X2IgRBEKRybRxajkPX0oGQz59YPtiN0C8B6R1WhlTEyZnus9ajZ2TCvVvX6NK8Fm9evUjXmHT19Bk2aS7TFq/D2NSMe7dv0aC6I5vWLieFn1EKQrrauHoZAFWdG2os8RMEQUiuFCd/LVu2ZObMmYwePZpixYrh7e3NkSNHyJIlCwCvX7/mw4cPCdcvWbKEqKgoXFxcsLKySnjMnDlTda9CEAQBkOkakqPdFLRMLPn05iUrhnYRTeATkaNIKfos3IZ51uy88XlB+6bVuXMj6aJd6lbVuSGbDl6gdPnKREZ8ZfSQfnRt1xQ/3w9J3ywI6SzwcwD7dioLK7m065zO0QiCIPwoxds+04PY9ikIfxZ1bPv8twj/1zxb5UHs12DylK5E5ynLkGuJ82M/ExzwiVXDuvLm8V3k2tqMm7mUmvWapHdYxMXFsWXNEhbPGE9UVCTGpmZMmD6feo2apXdogpCoRbOnMmfaePIVLMravac1WlFXbPsUhD9Lhtn2KQjC361hw4bY2tqiq6uLlZUV7du35/379+kd1nd0M9vi0GYSUi1dnlw7x5YpQ4iLi0vvsDIk40wWuM/bRIHy1YmJimJEXzfWLJmd7lstpVIpbTr1Yu2eU+QtWITgL4H069aevl3b8/k/zdAFISMIDwtj7YolALTp0jtdW6kIgiAkRiR/giCkSNWqVdm2bRuPHz9m586dPH/+HBcXl/QO6wcG2fNj12I0SGXcOrmfPfPHp3tCk1Hp6OnjNnEJlVw6ArB45ngmDO1FVGRk+gYG5MxbgFU7TtClzxBkMhmH9u2kjlMpjhzYk96hCcJ3tqxfxeeAT2SzsaNG3fRfPRcEQfgZkfwJgpAi/fv3p1y5ctjZ2VG+fHk8PT25fPky0dHR6R3aD4xzlcG28VBAwoXd6zm2dkF6h5RhSWUyGvcZRROPsUikUg7s3ESfjk348jn9i+ZoaWvTzWM4K3ecIEfu/AT4+9G7cxv6dG2Hv59v0gMIgpqFh4WxdMEsADr2GCDaYwiCkGGJ5E8QhFT7/PkzGzdupHz58hm26bNZ4WpY1+kFwLHV8zi3Y036BpTBVWzSni5TV6BrYMitqxdxa1ad508epndYABQoUpx1e0/j1nMQMpmMw/t2UatSCXb/r707D4uq+uM4/h5mYABlcwFRcQEXzI0UxX0vzd1yyRXLXHIJtUxNy/q5l+a+pJaauZSm5r5ruaWpuOUuKoqAK4IbMDPn94dBoWhgwIXh+3qe+/hw59zhc48zc/jOvffcnxbLUV2hqQVzpnP71g0KFCpC07c6aB1HCCGeS4o/IUSqDR48mBw5cpA7d25CQ0P55ZdfXtg+NjaW6OjoJEtGylO5JR51AgFYPW0khzatzNDfn9X4BtSm38wV5M5fiLDQy3R96zX27NysdSwA7IxG3v9wOAtW7aDEK2WJjrrLoH7deeftFoRevqR1PJEN3boRyTfTvwag54BhGDLpF2FCCAFS/AkhgCFDhqDT6V64nDlzJrH9oEGDCA4OZsuWLej1erp06fLCIy9jx47FxcUlcfHyyvibr3vU6kSegDcBWDpuMCd2b8nwDFlJviLF+WDWz/j4BRD78D4fdn+b77+ZkmmOsJUsXZ4FK3fQ+6PPsLMzsmfXNt6o7c830yZmylOQhfWaMGYED+7H8Eq5CrzeVGajFUJkbnKrByEEN2/e5PbtF1/b5e3tjZ3ds7dLuHbtGl5eXuzbt4+qVasmu21sbCyx/5g8JDo6Gi8vr3S71cPzKGXh6pqJ3D26GZ3elu7j51GyUo0M+/1ZkSk+jlVTvuD3tcsAeL1Za4aPnYq9g6PGyf4WeukiY4f35/DvuwEo4VuakV9NpWLl5F+PQqSVI3/8Ttum9QCYt3wL5SpU1iyL3OpBCOsit3oQQqSbvHnz4uvr+8IlucIPSLyFQuwLZoY0Go04OzsnWbSg09ng1WwgLqVqoszxzBvak0snDmmSJasw2NrR+sNRvNn/C2z0BrasXUH3do0IDwvVOlqiQkV9mPnDGj4bPwMXt1ycO/Mn7ZrVZ0j/Xty+dVPreMJKxcXFMfyjfgA0a91R08JPCCFSSoo/IUSKHThwgOnTp3P06FGuXLnCjh07aN++PT4+Ps896pfZ6Gz0FHpzKE4+/ljiHzPzw3e4evaE1rEyNZ1OR/VWnej19ffkdM3F2T+P06FZHQ7t/03raIl0Oh1NW3dk+dZDNG/bGYAVS7/ntWrl+WH+N5jNZo0TCmszc/J4zp35E9dcuek3+H9axxFCiBSR4k8IkWKOjo6sXLmS+vXrU7JkSbp160a5cuX49ddfMRqNWsdLMRuDHUXafU6OwuWwxD5kWlBnwkPOah0r0/PxC6D/nF8oWKI0D+7doW9gKxbPm5ZprgMEcHXLxfCx05i3fMuTCWHuRfH5kAG0fL06f/y+V+t4wkocDz7ErMlfAjBoxFe45sqtcSIhhEgZueZPCJHhEt7TGX3N39PMsQ8IWTSYh2FnMORw48PZP+FeyFuzPFlFfOxjVkwczqHNqwBo0LgVw8dNwzFHTo2TJWUymVi1dD6zvx5FTPQ9ABo3f4vBn42mgFchjdOJrOr+/RhaNKjGlUsXadC4FaOnfodOp9M6llzzJ4SVkWv+hBAijemNOSjacSz2Hj6YHtxl9sDO3L6eea5ly6xsjfa8PfQrWvX/HBu9gW0bVvHOm/W5fPGc1tGSMBgMtOncnRXbDtOq/TvodDo2rPmZ16v78fXYz3nw4L7WEUUWo5Ti04/6ceXSRTw8CzJ45NeZovATQoiUkuJPCJGtGRyc8Ok8HmPewty7GcGs/h25ExGmdaxMT6fTUaNVZ3pPXYJzHg8uXThL5xZ12bou891D0S13HoaOmsSiNb9SIaA6sbGPmTn5S+oHlGHZou8wmUxaRxRZxKJvZ7N21U/o9XpGTZ6Hi6ub1pGEECJVpPgTQmR7hhyu+HT+EmPugtyNvM7sAZ2IuhGudawsoWiZigycu4Zir1Yh9tEDhgW9y1efDyLuBbO/aqXEK+WYtXgd42cuomChoty6eYPhH/WlSd3KbNu0LlNduygyn/27dzH6s48B6Dv4C8r7V9E2kBBCvAQp/oQQArB1yo13l6+wc/Pk9vVQZg3oxL1bkVrHyhKccuWhx4SF1OvYC4Dli+bSvV0jwq5e1jZYMnQ6HXUbNuPHzQcYMHwMzq5uXDx3hl6BbXm7eQMOH9yvdUSRCV08f5be77bHbDbTqEVbOrzbR+tIQgjxUqT4E0KIv9g558UncAJ2rvm4de0yswZ0Ivr2Da1jZQl6g4EmPQbRbdw8HJ1dOX0imPZNa7Jz81qtoyXL1s6O9u/0ZtXOYAJ7DcBotOfwwf20a1af7h3f5M8TR7WOKDKJiPAw3m3fgpjoe5R9tTLDxk6V6/yEEFmWFH9CCPEPdi4e+AROwNbFnZuhIczq34no23Kj8JR6pWpdBs5bS+FXXuXx/RgG9+6caU8DBXBydqXPoBH8vOMIrd7uil6vZ+e2TbRoUI2+73Xk3JlTWkcUGrp96yZd2zUn7GooXkV8mDhnKUajvdaxhBDipUnxJ4QQT7FzzfekAHTOy43Qi8zq31EKwFRw88hPn2lLqfN2d+DJaaDvtm7AlZDzGid7Pvd8+Rk6ejI/bj5Iw+Zt0Ol0bFq7iiZ1KhHUo4sUgdnQ3Tu36dq2KRfOniavhyfTFq6U+/kJIbI8Kf6EECIZRrf8+AROlALwJekNtjR7fwjvjZ9HDpdcnDt1go7NarF2xQ+ZemKVQkV9GDlpLkvW76Veo+YopVj/ywoa1/anT7cOnDp5TOuIIgPcuhFJ57cac/rPE+TK486MRb+Qv2BhrWMJIcR/JsWfEEI8hzFXcgWgXAOYGqWq1OXD79ZRrEJV4h4/YuTgvgz74F2i70VpHe2FfEq+wrgZ37N4/R7qNWoOwOZ1q2levyrvdWwlE8NYsatXLvN2i9c4c+oEufN6MGvxWor4lNA6lhBCpAkp/oQQ4gWMufLj0/XvAnBmUAfu3YzQOlaW4pLHg54TFtK4+0eJN4Xv2KQGRw7u1TravyruW4ZxM75n6cb9vN6sNTY2Nuzatpl2zerzdvMGbN+8HovFonVMkUaOBx+iTZM6XA65gGfBQsxZtpGixUpqHUsIIdKMFH9CCPEvjG758en6NbYuHty8eomZQR24G3ld61hZio1eT/1O79Nvxk/kLlCIyPBrvN+hKTO++oL4uDit4/0rnxKlGDV5Hsu3HqJlu0Bs7ew4dGAfPbu04Y1aFVn2/bc8fvRI65jiP1i/egXtW7zOrZs3KOZbmnk/bcariLfWsYQQIk1J8SeEEClgdPOkWNevn9wGIuwKMz9oz+3wq1rHynIKlSrPwHlrqdy4DUopFs6exLutG3Dx3Gmto6WIVxFvPhkzhdW7jtG5RxA5cjpz8fxZhg/qR82KJZk4ZgQR4WFaxxSpEB8fz7gvPiGoZxdiYx9Tvc7rzFm2kbwenlpHE0KINCfFnxBCpJCdqwc+Xb/GLlcB7kRcY+YH7bl17bLWsbIce8ectBs8jsCRM3F0cePsn8fp3KI2i7+dnmVOoczr4Um/wV+wds9J+g8bjWcBL+7evsWsKV9R278UQT268MfvezP15DYCwq6G0unNRsybORmATt0/YMKcpeR0ctY2mBBCpBMp/oQQIhXsXNwp1nUixjyFiLoRzowP2hNxOfPewiAzK1erIYPmb8A3oDamuDimjBnO+x2bEhZ6WetoKZbTyZkO7/bh5x3BjJuxEL9KVTGbTKz/ZQXtW7xG07oBLPpuNjHR97SOKv5BKcXqFUtpUrcyhw/uJ0dOZ8bP/J4PhvwPvV6vdTwhhEg3UvwJIUQq2TrlwSdwIvbuRYm+fYNJ77/N9QtZ47TFzMY5tzvvjf+W1h+OxM7BkeCD+2jXuBo/L/kuSx01MxgM1GvUgjnLNvLD2t9o0bYLRnsHzp4+yRdDB1K1nA9Dgnpy+OD+LLVf1igiPIxegW35qE837sdEU8bPnx/W/kbdhs21jvafhIeFah1BCJEF6FQWGIWio6NxcXHh3r17ODvLqRhCZHUJ7+kyQ35Bb8yhdZyXZnp4j5AfhvIo/Bx6+5z0mbSQwq/4aR0ry7p9PZRl4wYTcuwgAJWq1WbY2KlZ9v5qMdFRbFi5jJVL53PpwtnE9d7FSvBmu060bNOefJ4FNEyYvZhMJn747hsmjf8fD+7HYLC1pVufQQS+PxCDwaB1vP/kZmQ4zWuXwxwfL38rCWEl0qv+keJPCJHhrKX4AzA/vk/IkmE8vPonNnYO9PxyHsVeraJ1rCzLYrGw5+eFbJg7gfjYx9g5ONJ/yP94s8O72NhkzZNVlFIcP3yAX376nm0bVvP40UMAdDod1WrVo8Vb7XitcXOc5DqzdKGU4redWxn3+SecP3sKgDJ+/nwyZgrFSpbWOF3a+OrzQSxfNBdA/lYSwkpI8SfFnxBWw5qKPwBz3CMuL/uM+5eC0Rns6DZ6JqWq1NU6VpZ289olfho/lJDjfwDgV6kqw8ZOo3DRYhon+2/ux0SzfeNq1v28lGOH/r5RvNFoT93X36BJi9bUqd8QB0dHDVNaj+BDB/l67Ofs37MLABe3XPT+8DNatOuSZb9MeNr1a1d4q74/ZlM8IMWfENZCij8p/oSwGtZW/AFYTHFcWT6S6HP7wUZP508n4VevidaxsjSLxcK+1T+wfs5XxD16iMHOjp5BQ+nYrS8GW1ut4/1nYaGX2fjLj2xes4IrIX9PGmTv4Ejd1xrRqElLatV/XY4IppJSij9+38usKV+ye+c2AGzt7GjTuTvv9hmEs4urtgHT2GcDe7Dpl5/w9qtMyNGD8reSEFZCij8p/oSwGtZY/AEos4nQ1eOJOrkT0NHmo1FUafa21rGyvDvh11g+cTjn/tgNQPFSZRg2ZiqvlKugcbK0oZTi7J/H2Lp+Fds2rCL82t8Td9ja2VGlei0aNGpK3QZvkL+gl4ZJM7e4uDg2r1vNgjnTORZ8CAC9Xk/jN9vzXr+P8SxQSOOEae/U8SN0bVUPgPenLGFWUAf5W0kIKyHFnxR/QliNhPd0yb4Lsc9tXRNeKIuZsA3TuH14HQBNen5MvQ49NU6V9SmlOLx5Fb/MGM3D6Ch0Nja06fQevQYOt6p7simlOH0imJ2b17Jz81pCL11I8ngJ39LUqvcaNes0wD+gGkZ7e42SZh4hF86xYukifl62iNu3bgBgZ2ekyVsd6NIjiAKFimgbMJ1YLBbea9uQk8F/4N+wFa2CRjCssZ/8rSSElZDiT4o/IaxGwnvamLcoxd75GoODk9aR0pRSiojt33Jj7zIA6rbvQZOeH6PT6TROlvXdj7rNL9NHc2TrL8CTm60P/HQc9Ro1t7r+VUpx+eI5ftu+kT3bN3Ei+CAWiyXxcaO9Pf4B1alaozYB1WpRpvyr2FrB6bApEREexqa1q1m76ieOHfkjcX1eD09ate/Km+3fJVeevBomTH9rli9i1JB+GB1yMPiHrRgdHKX4E8KKSPEnxZ8QViPhPQ3gWLAU3p2/RG/noHGqtHdj74+Eb3syA1/lxm1o/eEo9Fl8SvnM4uwfu/l50mfc/uveZtVqv8ZHI76kYOGiGidLP/ei7nJg9w72/7aNA3t2cutGRJLHHR1z4FexMhUqV+FV/wD8KlTCxdVNo7Rpy2KxcPrP4/y6bTPbt2xIUvDp9Xqq1KxP87adqFnvDau4HvTf3L19i1YN/HkYHUWz3kOp0+49Hj+IkeJPCCsixZ8Uf0JYjcTiz+AIpofkLPoqRTuMxsZgp3W0NHc7eCPX1k4CZaF0jQZ0/mwKtkY5VS8txMc+ZvsPs9ixdA7m+DgMdna88/5AOvcIwt7e+r5M+CelFCHnz3Bo368c+n03wX/sIzrq7jPtingXo2z5CpQu58crZcrjW7osuXLn0SBx6phMJs6d+ZMjf/zOwX17+H3vb9y5fTNJm3IVAnitSSvqN2lFnrweGiXVxvD+77Fl7Qo8fXwZMGc1eoOtFH9CWBkp/qT4E8JqJLyn7WoNIm7fNDA9xql4AEXafY6N3vq+tb93Zi9XVoxCmePxLleJd8fMwcGKrlPT2o3QEFZO/pzzh/cCkN+rMAOHj6Vm/Tes7lTQ57FYLFw6f4bgQ/s5ceQAJ4MPcfVKSLJt87p7ULzkK/gUL0nRYsUp6lOcQkW8yV/AS5PTRu9F3SXkwnnOnz3FmT9PcOrkMU6dOMbDhw+StHNwzIF/1ZpUr9OQWg3eII97vgzPmhns3LyGwb27oLOxIWjWz3j5lgOQ4k8IKyPFnxR/QliNhPe0Q4sZWKJCid0zCcxxuLxSi8JvDUNno9c6Ypq7f/kYl5Z9iiX2IZ7eJen+1Xxc8mSvoxXpSSnFsZ0bWDNzDPduPjkdsmqtBgwYPoYiPiU0TqeNqLt3OH38CKdPHuXsn8c4d/oEYaGXn9vexsYGD8/8eOYvSD7PArjn8ySvuwe5cufB1S0Xrm65cHJyJkdOJxwdHTE6OGBra4fBYEi8Z57ZbCY+Lo64uFgePXrIg/v3uR8TTVTUXe7cvsXtmzeIjAgnIjyM61dDCQ29zN3bt5LNkyOnE2X8/PHzr0qFKjUoU94fWzvrOzsgNW7djKRNw6o8uHeHeh170aTHoMTHpPgTwrpI8SfFnxBW45/Fn87WAXPESWL3TQWLCbdyDfBqMcgqC8BHERcJWTwU0/07uOUrQPcv5+NR2EfrWFYl9uEDtv0wk19//BazKR4bvYG3u/akW99BODm7ah1Pcw8f3Cfk/BkuXTjD5YvnuRJynquXL3L96hViYx9rliuvhydFi5WkmG9pSpQqi28ZPwp7F0evt77PgZdlsVgY0K0t+3/bhqePL/1nr8RgZ0x8XIo/IayLFH9S/AmRqcTGxhIQEMCxY8cIDg7Gz88vxds+XfwBmK4HE7d/BigLuV59g4LNBqDT2aRTeu3E3g0n5IchxN0JQ+/gxPsTvqVomYpax7I6N69dYs30MZzavwMA11y56TlgGC3adsEgk+48w2KxcOfWDcLDrhIZHsaNiDBu3Yjkzq0bRN25zb2oO0Tfi+JBTDQPHtwn9vGjf31OvcGAg4MjOZ2ccXJxxdUtN7nyuJMnrwfunvnJl9+LAl6FKVjYG8ccOTNgL7O277+ZwvQvR2CwMzJgzmryFU16RFuKPyGsixR/UvwJkakEBQVx/vx5Nm7cmCbFH4Dp6kHiDnwDKHJXakGBN/pa5TVbpgdRXFo6nIdhZ9AZ7Oj6xVTK1HhN61hW6cyBX/ll+mhuhF4EwLt4KYKGjqRq7QYaJ8vaLBYLcXGxmOLjMMWbSPhTwkavR6/XY2/vkC1m3cwoRw7upXen5ljMZlp/OIqqzds/00aKPyGsS3rVP9b3tboQIt1t3LiRLVu2MGHChDR9XoNXZewqdQN03P7jF65vmU0W+H4q1Qw5XPHu8hVOxQNQpjjmD+/NvtWLtY5llXwDavPR/PW0ChqBo7MrIedPE/Rua/oFtuLc6RNax8uybGxssLd3IKeTC665cuOWOw9uufPg4upGTidnKfzSUOT1a3zUuwsWs5kKr7WgSrO3tY4khMjCpPgTQqRKZGQk3bt3Z9GiRTg6Ov6n50qusDMUroZdxUAAbv3+M+Hb51llAai3c6Do2/8jV4XGoCz8POkz1s0en+Qm3iJt6A221HizC0OX7KB2227obe04sGcnnZvV4vOPehH+170ChchsHj18wKBeHbl/9zb5i5WizUejrfJsCCFExpHiTwiRYkopunbtSq9evfD390/xdrGxsURHRydZAOJP/ZJ8AVi0Fravdgbg5t4fidi5IE3yZzY6Gz0Fmw4gX92uAOxcOofFIwcQHxurbTAr5ejkQvM+nzD4+8341WuCUooNq5bxZn1/Jo8ZRtSd21pHFCKR2Wzms4E9OPPnMXK45OKdUbOxs/L7Vwoh0p8Uf0IIhgwZgk6ne+Fy5swZpk2bRkxMDEOHDk3V848dOxYXF5fExcvLCwDzha2YTq9Ndhtbn7rYln9yXcuN3YuJ2LXwv+1kJqXT6fCo1Qmvlh+DjZ6jO9Yx56NAHtx79obdIm3kzl+IziOmEjR7FcVerYI5Po4l386gWe3yzJ06jvsx0VpHFNmcUoqvRw7h163rMdjZ8c7oWeTyLKh1LCGEFZAJX4QQ3Lx5k9u3X3zUw9vbm7Zt27J27dokpx2ZzWb0ej0dO3Zk4cLkC7TY2Fhi/3E0Kzo6OrEABLAt2wbbkm8ku238uc3EH/8RAI86geSr3TnF+5XVxIQc4fJPX2CJfUBer6K8N/5b8hQorHUsq6aU4uwfu9kwZwJh5/8EwMUtF1169Kd1p244OObQOKHIjuZOHcfcKePQ6XR0+mwKfvWa/Os2MuGLENZFZvuU4k8IzYWGhiaesglw/fp1GjZsyIoVKwgICKBgwZR9M53wntZ7N8Acsg0A2/JvY1v89WTbx5/dSPyJ5QDkq9MVj9qd/uOeZF6Pb1wmZMknxN+7gd7Rhfe/nEPRsik/xVa8HIvFwvFdG9k0fzI3Q0MAyJXHncBe/WnV/h3s5XQ7kUEWz5vGlLGfAtAqaAQ13uySou2k+BPCushsn0IIzRUqVIgyZcokLiVKPLnPlI+PT4oLv38yFKmN3vvJlPvxx5YRf2F7su1sS76BbZnWAETsWkDkbz+85B5kfvbuRSjebRoOniUwP7zHjKBOHNm2RutYVs/Gxga/ek0YNH8j7YaMJ5enF3du3WDSqE9oVcePpfNn8vjRQ61jCiu35LsZiYVfo3f7p7jwE0KIlJLiTwihKYPP6+iL1gUg/uhi4kN2JdvO1rcxtmXeAiBi5wIif7XeAtDWKTc+XSfi7FsdZY5n8cgBbFkwzSpnPc1s9AYDld9ozZAfttLmo9G4eeTn9s1IJo36hJa1y7NozlQePrivdUxhhRbM+prJo4cB0KBLHxp06atxIiGENZLTPoUQGS7hPW2sNxKdwR6lFKZz6zFf+RUAu4pdMRStley28Wc2EH9yBQAetbuQr471fjOulIXwrXO5uf/JKa+v1m9Gu8HjsTUaNU6WfZji4zi0aSXbf5jFnYhrADi7utEusCdtu/TExdVN44Qiq1NKMW38CH6YOxWA17t+wOtdP0j1LR3ktE8hrIuc9imEsFo6nQ5DiSboC9UEIO7wQkyXdifb1ta3MbZl2wAQ+ev3ROxcYLVHxHQ6G/K/3pOCTQeAjZ7g7WuZ1b8jMXduaR0t2zDY2lGl2dsMWbyNdkPGk6dgEaKj7jJ3yjia1CjNpNGfEHn9mtYxRRYVHxfH5x/1Siz8mr4/hIbvBMm9/IQQ6UaKPyFEpqDT6TCUbIa+UHVAEXd4AabLe5Jta1vyDWzLtgUg8rcfiNjxndUWgAC5KzbBu9M49PY5uXIqmMk9W3L9wmmtY2UreoMtld9ozeDvt9BpxBTyFytF3KOHLP1uJi3q+DHiw56cP3NS65giC4m6e4d+XVuxcfWP2Oj1tBs8nrpvd9c6lhDCyknxJ4TQjFKWJD8/KQBboPf6qwA8NP8FBWAjbMu/DcCNPUsJ3zrHqgtAp6KvUvy96RhzFyTqRjiTerXmxG+btY6V7djo9bxarykD562l+5ff4eMXgMVsYuPqH+nYpAb9Alux/9dtWCyWf38ykW1dOPsn77xZjyMH9mJ0zEm3cfOo3Li11rGEENmAFH9CCM2Yzq17pmDT6XQYfFug96rG3wXgc04BLf46tn4dAbi5fznXN8206gLQmLsgxbpNI6d3RSzxj1nwaW+2fj/dqvc5s9LpdPgG1Kb3lCUEzV5F+bqN0dnYcGDPToLebc3bjaqwYvG3PHr4QOuoIpPZtGY5Xd9sQFjoZXJ5etFvxk/4Vk7+GmchhEhrMuGLECLDJbynAfSFqmMo2eKZa1yUUpjOrMZ8dR+g+2sSmJrJPp8pZBdxR74HIHfFphRo8gE6nfV+t6UsZq5vnsWtg6sBKF+3Me0Gj8fo4KhtsGzuTvg1dv+8gAPrlxP78MmMoE7OLjRt3ZHWHd/Dq4i3xgmFlh4/esjXI4ey+seFAJTwr0GnzyaTwyVtJg2SCV+EsC5yk3cp/oSwGv8s/gD0hWpgKNn8OQXgL5iv7gXArkIgBu/ayT6n6fJu4g4tABRufg3xajYQnY0+vXYhU7h9eD1hG6ahLCbyF3uFd0bPJle+AlrHyvYeP4jh4MYV7F25iFthVxLXV63VgLc6vku1Oq9jMBg0TCgy2pmTR/lsYA8uXzyHTqejfufeNOwahI0+7T6jpPgTwrpI8SfFnxBWI+E9rS9cH/OVJzd21xeuiaFEs+QLwLNrMIc+ufbP9tXO2PrUTfZ5TaG/E/fHPFAWXMvUpVDLwej01v1H9v0rJ7jy0xeYHkahd3Sh59hZ+PgFaB1LABaLhbMHf2XPykWcPfhb4um57vkK0LxtJ5q36US+/F4apxTpKT4ujgWzv+bb6ROwmE0453an/bAJlKhYPc1/lxR/QlgXKf6k+BPCaiTe569iEOY7pzFd2gL8SwF4bi3mK0+u/bP164BtsQbJPrfp2iHiDnwDyoxzyWoUbj0cG4Nd+u6QxuLuRXL5x895FH4ebPS07DuMGm92keniM5FbYVfYv2Ypf2z8mQf37gBPrhusUrM+zdt2pma9RtjJ/RutyvEjBxk7rD8Xz50CoFztRrT+cFSaneb5NCn+hLAuUvxJ8SeE1fhn8aczGDHdOPp3AVioJoaSzykAz6/HfPnJjeBty7XFtkSjZJ/fHH6M2P0zwGIip09Firb7Ahtb+/TdKY1Z4h9zde3XRJ3YAYB/ozdpPXAktkbr3u+sxhQXy/HfNnNg3Y9cCP49cb2LWy5eb/oWTd7sQKmyflK4Z2FRd24zc8L/Eq/ty+GSi1ZBn+FXr2m6/r9K8SeEdclUN3mfMWMGRYoUwd7enoCAAA4ePPjC9suXL8fX1xd7e3vKli3Lhg0bXiqsEMI6Gdz9MBR9HQBz6G5MZ9ckPwto8Sboi9YHIP74T8SfXpfs8+k9y2OsMQD0Ru5fPEzID0Mxx1r3rIs2tvYUajWU/K/3Ap0NhzatZHq/dtyNvK51NPEPBjsjFRo05/3Jixm6eDv1O76Pcx4P7t29w/JFc+naqi5vv1GVBbO+JjwsVOu4IhXiYmNZ8t0MWtR9NbHwq9ToLT7+fjOv1n/2Cy0hhNBCqo/8/fjjj3Tp0oXZs2cTEBDA5MmTWb58OWfPnsXd3f2Z9vv27aNWrVqMHTuWpk2bsmTJEsaPH8+RI0coU6ZMin6nHPkTwro8feQvgenGMUyXnty7Tu9VHYPvs7OAApgubsV08cmRQkOpZti+0jLZduZbF4jdOwniH+GQvwTeHcdicHR5pp21iQk5wpUVozA/ikbv6MJ7o6alyzVGIm1YzGbOHdrDH5t+5uSebZjiYhMfK1+xCq81fZP6jVuSO8+zY6zQntlsZsvaFXwzeQzXrz6Z4Cd/sVK0+mAE3uUrZVgOOfInhHXJNKd9BgQEUKlSJaZPnw48uaDdy8uLfv36MWTIkGfat2vXjgcPHrBu3d/f0FepUgU/Pz9mz56dot8pxZ8Q1uV5xR+A6cZxTJc2AaAvWAVDqVbJ3rbBdGknpvNPziIwlGiEbdk2yRaAlrtXeLx7IsTdxz5vEbw7j8PWKU867FXmEhcVyeWf/roOUGdD056DqNu+h9axxL94dD+G479u5MjWX7h49EDiEXCdjQ0VKlfnjZZtad6ms8YpRYLd2zcy/cvPuXThLADOud1p1G0AlRq9laYzeaaEFH9CWJf0qn9SNQ1eXFwchw8fZujQoYnrbGxsaNCgAfv37092m/379zNw4MAk6xo2bMjq1auf+3tiY2OJjf37m8979+4BTzpBCJH1JbynlTn2mcf0uUqCMmO6vBUV+xhlioVkijq9V1WUAvOFDVhiH6LiHyXbTpfTHWON/sTum87jR4+wxMdZ/SmgAHqHnBTtMIbrW2YTdWI7B05coWrzGK1jiX+h00H5Om9Qvs4bRN+6wfHdWzjx6yaunTvJ4d9380hnS71GLbSOKf6y88gxLl04i31OZ2q+FUjV5h0wOjgQ9/hhhmd5/Ne9JRM+X4UQWVtC3ZPm07OoVAgLC1OA2rdvX5L1gwYNUpUrV052G1tbW7VkyZIk62bMmKHc3d2f+3tGjBihAFlkkUUWWWSRRRZZZJFFlmy7XLx4MTXl2r/KlDfAGjp0aJKjhVFRURQuXJjQ0NAkN4bOrqKjo/Hy8uLq1atyasdfpE+Syuz9YbFYCA8PJ2fOnP95EoSYmBheeeUVTp06hZOT039uZ+0S+uHAgQMEBARw5coVXF1dtY6VaWX299LTwsPD8fX1ZevWrVSuXDlx/aeffsrevXvZsWPHM9vkzp2b2bNn06ZNm8R1c+fOZdy4cVy8eDHZ35PcGTplypRJfF3J+yzjP5eUUty/fx9PT09sbF5qPr90ldXeS+lN+uNZ0idJ3bt3j0KFCpErV640fd5UFX958uRBr9cTGRmZZH1kZCT58uVLdpt8+fKlqj2A0WjEmMz9jlxcXOTF8A/Ozs7SH0+RPkkqM/dHWhUcCadFFChQ4IX7mtJ21i6hH/Lnzw88+X/Izv2RUpn5vfRP9vb26PV67t+/nyRvVFTUc1/7np6exMTEJHksOjqa/Pnzp3ifE9olvK7kfSafS8+TVd5LGUX641nSJ0ml9Zc5qXo2Ozs7KlasyPbt2xPXWSwWtm/fTtWqVZPdpmrVqknaA2zduvW57YUQQgjxcmScFkII8SKpPu1z4MCBBAYG4u/vT+XKlZk8eTIPHjzgnXfeAaBLly4UKFCAsWPHAhAUFETt2rWZOHEiTZo0YdmyZRw6dIg5c+ak7Z4IIYQQQsZpIYQQz5Xq4q9du3bcvHmTzz77jIiICPz8/Ni0aRMeHh4AhIaGJjk8Wa1aNZYsWcLw4cP55JNPKF68OKtXr07xPf7gyWmgI0aMSPZU0OxI+uNZ0idJZaf+SOm+Zqc+eZGEfnB2dpb+SIGs+LrRcpyW19UT8rn0rOy0rykh/fEs6ZOk0qs/Un2fPyGEEEIIIYQQWU/mmw5KCCGEEEIIIUSak+JPCCGEEEIIIbIBKf6EEEIIIYQQIhuQ4k8IIYQQQgghsoFMU/zNmDGDIkWKYG9vT0BAAAcPHnxh++XLl+Pr64u9vT1ly5Zlw4YNGZQ0Y6SmP+bOnUvNmjVxc3PDzc2NBg0a/Gv/ZUWpfY0kWLZsGTqdjpYtW6ZvwAyW2v6IioqiT58+eHp6YjQaKVGihNW+b4xGIzly5ECn03H06NHntp88eTIlS5bEwcEBLy8vBgwYwOPHjzMucDr67bffaNasGfnz50en07F69eokj1++fJlu3bpRtGhRHBwc8PHxITAwED8/P4xGI8WKFWPBggWaZM9MXvZzxxq9qC/Gjh1LpUqVcHJywt3dnZYtWzJlyhQZp//yb+P0uHHj0Ol09O/fPwOSpx8Zp5OScfpZqe2T7DxOJ2fXrl1UqFDhv43TKhNYtmyZsrOzU9999536888/Vffu3ZWrq6uKjIxMtv3evXuVXq9XX375pTp16pQaPny4srW1VSdOnMjg5Okjtf3RoUMHNWPGDBUcHKxOnz6tunbtqlxcXNS1a9cyOHn6SW2fJLh06ZIqUKCAqlmzpmrRokXGhM0Aqe2P2NhY5e/vrxo3bqz27NmjLl26pHbt2qWOHj2awcnTzz/7pFOnTsrLy0sBavv27cm2X7x4sTIajWrx4sXq0qVLavPmzcrT01MNGDAgg5Onjw0bNqhhw4aplStXKkCtWrUqyeMbN25UXbt2VZs3b1YXL15Uc+bMUYCqWLGiOnXqlJo2bZrS6/Vq06ZN2uxAJvCynzvW6N/6omHDhmr+/Pnq5MmT6ujRo6pq1aoKUKNGjZJxWr14nD548KAqUqSIKleunAoKCsrYHUlDMk4nJeP0s1LbJ9l9nH5aSEiIcnR0VAMHDvxP43SmKP4qV66s+vTpk/iz2WxW+fPnV2PHjk22fdu2bVWTJk2SrAsICFA9e/ZM15wZJbX98TSTyaScnJzUwoUL0ytihnuZPjGZTKpatWpq3rx5KjAw0KoGldT2x6xZs5S3t7eKi4vLqIgZLqFPNmzYoHx9fdWJEycUoPr165ds+z59+qh69eolWTdw4EBVvXr1jIiboVIyqHz88cfKw8NDFS1aNHFdu3btVMOGDdM5Xeb1Xz+LrUlq+6J58+YKUL/++mviOhmn/5YwTn/zzTeqePHiauvWrap27dpZuviTcTopGaefldo+kXE6qY8//liVLl06ybqXGac1P+0zLi6Ow4cP06BBg8R1NjY2NGjQgP379ye7zf79+5O0B2jYsOFz22clL9MfT3v48CHx8fHkypUrvWJmqJftk//973+4u7vTrVu3jIiZYV6mP9asWUPVqlXp06cPHh4elClThjFjxmA2mzMqdrpK6BN/f3+6d+/OokWLyJkzJwDHjx9Pdptq1apx+PDhxFNOQkJC2LBhA40bN86w3JnJ/v37KVSoUJLPDWv5XH0ZafFZbC1epi8S3lfW+HpKy3H6xx9/pEmTJs/8TZPVyDidlIzTz3qZPpFxOqm0qn8MaRnqZdy6dQuz2YyHh0eS9R4eHpw5cybZbSIiIpJtHxERkW45M8rL9MfTBg8eTP78+bP8YJLgZfpkz549fPvtty+83iurepn+CAkJYceOHXTs2JENGzZw4cIFevfuTXx8PCNGjMiI2OkqoU+++eYbevXqhb+/P5cvX058LDkdOnTg1q1b1KhRA6UUJpOJXr168cknn2Rg8swjNDSUiIgIpk2blrjOw8OD6OhoHj16hIODg4bpMl5afBZbi9T2hcViITIykhIlSlCmTJkk7WWcfmLw4ME4OzsTGRnJ2LFj0yNmhpJxOikZp5/1Mn0i43RSz6t/UjtOa37kT6StcePGsWzZMlatWoW9vb3WcTQRExND586dmTt3Lnny5NE6TqZgsVhwd3dnzpw5VKxYkXbt2jFs2DBmz56tdbR/NWTIEHQ63QuXCxcuAE++TR86dGiKnnfXrl2MGTOGmTNncuTIEVauXMn69esZOXJkeu5OukuuvwBatWqV+PPTA21YWBjXr1+nbNmydO/eXYvYwor06dMHpRT9+vXTOkqmNG7cOJYsWYLJZGLJkiXZcqyWcfpZWXmcTi/WOk5rTfMjf3ny5EGv1xMZGZlkfWRkJPny5Ut2m3z58qWqfVbyMv2RYMKECYwbN45t27ZRrly59IyZoVLbJxcvXuTy5cs0a9YscZ3FYgHAYDBw9uxZfHx80jd0OnqZ14inpye2trbo9frEdaVKlSIiIoK4uDjs7OzSNfN/8eGHH9K1a9cXtilYsCAAJ0+exGg0Jnns1KlTBAYGsnDhwiTrP/30Uzp37sx7770HQNmyZXnw4AE9evRg2LBh2Nhkze/GkuuvUqVKMW3atMSzAby9vRMfu379OnXr1sXNzY1q1aol2S4yMhJnZ+dsd9QP/ttnsbVJTV/07duXdevW4enpiclk+tf2WVFajNPDhw9n0KBBVKhQIfExs9nMb7/9xvTp04mNjU3yeZ3ZyTidVHYbp1PiZfrEWsfpl/W8+ie147TmvWZnZ0fFihXZvn174jqLxcL27dupWrVqsttUrVo1SXuArVu3Prd9VvIy/QHw5ZdfMnLkSDZt2oS/v39GRM0wqe0TX19fTpw4wdGjRxOX5s2bU7duXY4ePYqXl1dGxk9zL/MaqV69OhcuXEgcXAHOnTuHp6dnph9Q8ubNi6+v7wuXnDlzUr58edq1a5f4f75u3TrgyWkjo0ePfuZ5Hz58+MzAkTDoPrn2OmtKrr/gSYGc8HPC/3lYWBh16tShYsWKdOnShR07diR5Lmv5XH0ZL/tZbI1S0hdKKfr27cuqVavYsWMHNWvWlHH6Kf8cp3v27PnMOOXv70/Hjh05evRolir8QMbpp2W3cTolXqZPrHWcfllpVv+kanqYdLJs2TJlNBrVggUL1KlTp1SPHj2Uq6urioiIUEop1blzZzVkyJDE9nv37lUGg0FNmDBBnT59Wo0YMcLqppBOTX+MGzdO2dnZqRUrVqjw8PDEJSYmRqtdSHOp7ZOnWdssYqntj9DQUOXk5KT69u2rzp49q9atW6fc3d3VqFGjtNqFNPd0n7Rv314Batu2bUqpZ/tkxIgRysnJSS1dulSFhISoLVu2KB8fH9W2bVutdiFNxcTEqODgYBUcHKwA9fXXX6vg4GB15coVpdSTWdScnJxU/fr11bVr19SBAweUg4ODev/999Xp06fVjBkz5FYP//I+y07+rS9KlCihjEaj2rVrlwoPD1dr1qxRer1ejR07VsZplbJxOqvP9injdFIyTj8rtX2S3cfpIUOGqM6dOye2T7jVw6BBg/7TOJ0pij+llJo2bZoqVKiQsrOzU5UrV1a///574mO1a9dWgYGBSdr/9NNPqkSJEsrOzk6VLl1arV+/PoMTp6/U9EfhwoUV8MwyYsSIjA+ejlL7GvknaxtUlEp9f+zbt08FBAQoo9GovL291ejRo5XJZMrg1Onrn31Svnx5Bajg4GCl1LN9Eh8frz7//HPl4+Oj7O3tlZeXl+rdu7e6e/euJtnT2s6dO5P9XEjog+rVqyf7OKDs7OyUt7e3mj9/vqb7kBm86H2W3byoL573WvLw8JBxWqVsnM7qxZ9SMk4/TcbpZ6WmT7L7OB0YGKhq1679zDZ+fn7/aZzWKZUNj5sKIYQQQgghRDaj+TV/QgghhBBCCCHSnxR/QgghhBBCCJENSPEnhBBCCCGEENmAFH9CCCGEEEIIkQ1I8SeEEEIIIYQQ2YAUf0IIIYQQQgiRDUjxJ4QQQgghhBDZgBR/QgghhBBCCJENSPEnhBBCCCGEENmAFH9CCCGyndWrV6PT6Zg5c2aS9bNmzUKn01GkSJEk62NiYnBxcaFu3boZmFIIIYRIW1L8CSGEyHbc3NyAJ0VdAovFwqRJkwC4e/dukvYLFy4kOjqagQMHZlxIIYQQIo1J8SeEECLbSa74W7t2LefPn6d58+bExMRgNpsBUEoxffp0ihcvTtOmTTXJK4QQQqQFKf6EEEJkO66urkDS4m/ixIlUrFiRZs2aoZQiKioKgC1btnD27Fn69++PTqfTIK0QQgiRNqT4E0IIke08feTvjz/+YPfu3QwcOBAXFxfg71M/p06dipubG4GBgYnbT5kyhcKFC2Nvb0+NGjU4duxYBu+BEEIIkXpS/AkhhMh2nJycMBgMicXfxIkT8fLyom3btonF3507d7hw4QIbN26kZ8+e5MiRA4AlS5YwePBgRo4cyeHDhylWrBgNGzYkOjpas/0RQgghUkKKPyGEENmSq6srMTExXLlyhRUrVtCvXz8MBkOSI3/Tp0/HYDDQt2/fxO0mTZpEr1696NKlC6VLl2bevHmYTCaWLFmi1a4IIYQQKSLFnxBCiGwpofibMmUKDg4O9OjRAyCx+Lt69Srz58+nbdu2FChQAIC4uDiCg4Np0KBB4vMYDAbq1KnD/v37M34nhBBCiFSQ4k8IIUS25ObmRlhYGPPmzePdd99NLPoS/p06dSrR0dEMGDAgcZtbt25hNpvx8PBI8lzu7u5ERERkXHghhBDiJUjxJ4QQIltyc3PjypUrPHjwgKCgoMT1CcXfiRMnqFWrFhUrVtQqohBCCJGmpPgTQgiRLSXM+NmyZUu8vb0T1zs6OmIwGACSHPUDyJMnD3q9nsjIyCTrb9y4Qb58+dI5sRBCCPHf6JRSSusQQgghRFZRqVIlatSowaRJkwAwmUzky5ePUaNG0atXL43TCSGEEM9n0DqAEEIIkZUMGDCAbt26UbFiRSpUqMCECRMwGAx06NBB62hCCCHEC0nxJ4QQQqRChw4duHnzJp988gmRkZH4+/uzefNmnJ2dtY4mhBBCvJCc9imEEEIIIYQQ2YBM+CKEEEIIIYQQ2YAUf0IIIYQQQgiRDUjxJ4QQQgghhBDZgBR/QgghhBBCCJENSPEnhBBCCCGEENmAFH9CCCGEEEIIkQ1I8SeEEEIIIYQQ2YAUf0IIIYQQQgiRDUjxJ4QQQgghhBDZgBR/QgghhBBCCJENSPEnhBBCCCGEENmAFH9CCCGEEEIIkQ38H2suOn6P8mTmAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x450 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define constants for a N=2 input quadratic\n",
    "a = 20\n",
    "b = np.zeros((2,1))\n",
    "C = np.array([[2,1],[1,2]])\n",
    "\n",
    "# a quadratic function defined using the constants above\n",
    "g = lambda w: (a + np.dot(b.T,w) + np.dot(np.dot(w.T,C),w))[0]\n",
    "\n",
    "# initialization\n",
    "w = np.array([3,4])\n",
    "\n",
    "# run your alternating descent code\n",
    "max_its = 2\n",
    "weight_history,cost_history = coordinate_descent_for_quadratic(g,w,max_its,a,b,C)\n",
    "\n",
    "# show run in both three-dimensions and just the input space via the contour plot\n",
    "plotter.two_input_contour_plot(g,weight_history,xmin = -4.5,xmax = 4.5,ymin = -4.5,ymax = 4.5,num_contours = 30,show_original = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jx5QzlboOXC7"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 8:</span>  Solving systems symmetric equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gNv0wfZZOXC7"
   },
   "source": [
    "Note how in the previous example the first order system turned out to be *linear*.  More specifically, we ended up using coordinate descent to solve the linear system (re-arranging equation \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{C}\\mathbf{w} = - \\frac{1}{2}\\mathbf{b}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Y1tatd0POXC7"
   },
   "source": [
    "Here square symmetric $N \\times N$ matrix $\\mathbf{C}$ and the $N\\times 1$ vector $\\mathbf{b}$ came from an associated quadratic (and since that quadratic is assumed convex, $\\mathbf{C}$ must be *positive semi-definite*, i.e., it must  have all nonnegative eigenvalues).  However, divorced from the concept of a quadratic we can think of coordinate descent in a broader context - as a method for solving more general linear systems of equations where the matrix $\\mathbf{C}$ is positive semi-definite.  \n",
    "\n",
    "Thus we can re-interpret the experiments performed in the previous example in just this way - as examples of coordinate descent applied to solving square linear systems of equations where the matrix $\\mathbf{C}$ is positive semi-definite."
   ]
  }
 ],
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